Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus Enhanced with Graphing Utilities
find the real zeros of each trigonometric function on the interval 02 . f( x )=sin( 2x )sinxfind the real zeros of each trigonometric function on the interval 02 . f( x )=cos( 2x )+cosxfind the real zeros of each trigonometric function on the interval 02 . f( x )=cos( 2x )+ sin 2 xConstructing a Rain Gutter A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, the builder bends this length up at an angle . See the illustration. The area A of the opening as a function of is given by A( )=16sin( cos+1 ) , 0 90 (a) In calculus, you will be asked to find the angle that maximizes A by solving the equation cos( 2 )+cos =0,0 90 Solve this equation for . (b) What is the maximum area A of the opening? (c) Graph A=A( ), 0 90 and find the angle that maximizes the area A . Also find the maximum area.Laser Projection In a laser projection system, the optical angle or scanning angle is related to the throve distance D from the scanner to the screen and the projected image width W by the equation D= 1 2 w csccot (a) Show that the projected image width is given by W=2Dtan 2 (b) Find the optical angle if the throw distance is 15 feet and the projected image width is 6.5 feet. Source: Pangolin Laser Systems, Inc.Product of Inertia The product of inertia for an area about inclined axes is given by the formula I uv = I x sincos I y sincos+ I xy ( cos 2 sin 2 ) Show that this is equivalent to I uv = I x I y 2 sin( 2 )+ I xy cos( 2 ) Source: Adapted from Hibbeler, Engineering Mechanics: Statics, 13th ed., Pearson © 2013.Projectile Motion An object is propelled upward at an angle , 45 90 , to the horizontal with an initial velocity v 0 feet per second from the base of a plane that makes an angle of 45 with the horizontal. See the illustration. If air resistance is ignored, the distance R that it travels up the inclined plane is given by the function R( )= v 0 2 2 16 cos( sincos ) Show that R( )= v 0 2 2 32 [sin( 2 )cos( 2 )1] In calculus, you will be asked to find the angle that maximizes R by solving the equation sin( 2 )+cos( 2 )=0 solve the equation for . What is the maximum distance R if v 0 =32 feet per second? Graph R=R( ), 45 90 , and find the angle that maximizes the distance R . Also find the maximum distance. Use v 0 =32 feet per second. Compare the results with the answers found in parts (b) and (c).Sawtooth Curve An oscilloscope often displays a sawtooth curve. This curve can be approximated by sinusoidal curves of varying periods and amplitudes. A first approximation to the sawtooth curve is given by y= 1 2 sin( 2x )+ 1 4 sin( 4x ) Show that y=sin( 2x ) cos 2 ( x ) .Area of an Isosceles Triangle Show that the area A of an isosceles triangle whose equal sides are of length s , and where is the angle between them, is A= 1 2 s 2 sin [Hint: See the illustration. The height h bisects the angle and is the perpendicular bisector of the base.]Geometry A rectangle is inscribed in a semicircle of radius 1 See the illustration. (a) Express the area A of the rectangle as a function of the angle shown in the illustration. (b) Show that A( )=sin( 2 ) . (c) Find the angle that results in the largest area A . (d) Find the dimensions of this largest rectangle.101AYU102AYU103AYU104AYU105AYU106AYU107AYU108AYU109AYU110AYU111AYU112AYUfind the exact value of each expression. sin 195 cos75find the exact value of each expression. cos 285 cos195find the exact value of each expression. sin 195 cos75find the exact value of each expression. sin 75 +sin15Find the exact value of each expression. cos 225 cos 195Find the exact value of each expression. sin 255 sin 15express each product as a sum containing only sines or only cosines. sin( 4 )sin( 2 )express each product as a sum containing only sines or only cosines. cos( 4 )cos( 2 )express each product as a sum containing only sines or only cosines. sin( 4 )cos( 2 )express each product as a sum containing only sines or only cosines. sin( 3 )sin( 5 )express each product as a sum containing only sines or only cosines. cos( 3 )cos( 5 )express each product as a sum containing only sines or only cosines. sin( 4 )cos( 6 )express each product as a sum containing only sines or only cosines. sinsin( 2 )express each product as a sum containing only sines or only cosines. cos( 3 )cos( 4 )express each product as a sum containing only sines or only cosines. sin 3 2 cos 2express each product as a sum containing only sines or only cosines. sin 2 cos 5 2express each sum or difference as a product of sines and/or cosines. sin( 4 )-sin( 2 )express each sum or difference as a product of sines and/or cosines. sin( 4 )+sin( 2 )express each sum or difference as a product of sines and/or cosines. cos( 2 )+cos( 4 )express each sum or difference as a product of sines and/or cosines. cos( 5 )-cos( 3 )express each sum or difference as a product of sines and/or cosines. sin+sin( 3 )express each sum or difference as a product of sines and/or cosines. cos+cos( 3 )express each sum or difference as a product of sines and/or cosines. cos 2 -cos 3 2express each sum or difference as a product of sines and/or cosines. sin 2 -sin 3 2establish each identify. sin+sin(3) 2sin(2) =cosestablish each identify. cos+cos(3) 2cos(2) =cosestablish each identify. sin(4)+sin(2) cos(4)+cos(2) =tan(3)establish each identify. cos-cos(3) sin(3)-sin =tan(2)establish each identify. cos-cos(3) sin+sin(3) =tanestablish each identify. cos-cos(5) sin+sin(5) =tan(2)establish each identify. sin[ sin+sin(3) ]=cos[ cos-cos(3) ]establish each identify. sin(4)+sin(8) cos(4)+cos(8) =tan(6)establish each identify. sin(4)+sin(8) cos(4)+cos(8) =tan(6)establish each identify. sin(4)-sin(8) cos(4)-cos(8) =-cot(6)establish each identify. sin(4)+sin(8) sin(4)-sin(8) =- tan(6) tan(2)establish each identify. cos(4)-cos(8) cos(4)+cos(8) =tan(2)tan(6)establish each identify. sin+sin sin-sin =tan + 2 cot - 2establish each identify. cos+cos cos-cos =-cot + 2 cot - 2establish each identify. sin+sin cos+cos =tan + 2establish each identify. sin-sin cos-cos =-cot + 2establish each identify. 1+cos( 2 )+cos( 4 )+cos( 6 )=4coscos( 2 )cos( 3 )establish each identify. 1-cos( 2 )+cos( 4 )-cos( 6 )=4sincos( 2 )sin( 3 )solve each equation on the interval 02 sin( 2 )+sin( 4 )=0solve each equation on the interval 02 cos( 2 )+cos( 4 )=0solve each equation on the interval 02 cos( 4 )-cos( 6 )=0solve each equation on the interval 02 sin( 4 )-sin( 6 )=047AYU48AYU49AYU50AYU51AYU52AYUDerive formula ( 3 ) .54AYU55AYU56AYUIn Problems 1 and 2, find the exact value of the six trigonometric functions of the angle in each figure.In Problems 1 and 2, find the exact value of the six trigonometric functions of the angle in each figure.In Problems 3-5, find the exact value of each expression. Do not use a calculator. cos 62 sin 28In Problems 3-5, find the exact value of each expression. Do not use a calculator. sec 55 csc 35In Problems 3-5, find the exact value of each expression. Do not use a calculator. cos 2 40 + cos 2 50In Problems 6 and 7, solve each triangle.In Problems 6 and 7, solve each triangle.In Problems 8-20, find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle." A= 50 , B= 30 , a=1In Problems 8-20, find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle." A= 100 , a=5 , c=2In Problems 8-20, find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle." a=3 , c=1 , C= 110In Problems 8-20, find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle." a=3 , c=1 , B= 100In Problems 8-20, find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle." a=3 , b=5 , B= 80In Problems 8-20, find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle." a=2 , b=3 , c=1In Problems 8-20, find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle." a=10 , b=7 , c=8In Problems 8-20, find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle." a=1 , b=3 , C= 40In Problems 8-20, find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle." a=5 , b=3 , A= 80In Problems 8-20, find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle." a=1 , b= 1 2 , c= 4 3In Problems 8-20, find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle." a=3 , A= 10 , b=4In Problems 8-20, find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle." a=4 , A= 20 , B= 100In Problems 8-20, find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle." c=5 , b=4 , A= 70In Problems 21-25, find the area of each triangle. a=2 , b=3 , C= 40In Problems 21-25, find the area of each triangle. b=4 , c=10 , A= 70In Problems 21-25, find the area of each triangle. a=4 , b=3 , c=5In Problems 21-25, find the area of each triangle. a=4 , b=2 , c=5In Problems 21-25, find the area of each triangle. A= 50 , B= 30 , a=1Area of a Segment Find the area of the segment of a circle whose radius is 6 inches formed by a central angle of 50 .Geometry The hypotenuse of a right triangle is 12 feet. If one leg is 8 feet, find the degree measure of each angle.Finding the Width of a River Find the distance from A to C across the river illustrated in the figure.Finding the Distance to Shore The Willis Tower in chicago is 1454 feet tall and is situated about 1 mile inland from the shore of Lake Michigan, as indicated in the figure on the top right. An observer in a pleasure boat on the lake directly in front of the Willis Tower looks at the top of the tower and measures the angle of elevation as 5 . How far offshore is the boat?Finding the speed of a Glider From a glider 200 feet above the ground, two sightings of a stationary object directly in front are taken 1 minute apart (see the figure). What is the speed of the glinder?Finding the Grade of a Mountain Trail A straight trail with a uniform inclination leads from a hotel, elevation 5000 feet, to a lake in a valley, elevation 4100 feet. The length of the trail is 4100 feet. What is the inclination (grade) of the trail?Finding the Height of a Helicopter Two observers simultaneously measure the angle of elevation of a helicopter. One angle is measured as 25 , the other as 40 (see the figure). If the observers are 100 feet apart and the helicopter lies over the line joining them, how high is the helicopter?Constructing a Highway A highway whose primary directions are north-south is being constructed along the west coast of Florida. Near Naples, a bay obstructs the straight path of the road. Since the cost of a bridge is prohibitive, engineers decide to go around the bay. The illustration shows the path that they decide on and the measurements taken. What is the length of highway needed to go around the bay?34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE1CT2CT3CT4CT5CT6CT7CT8CT9CT10CT11CT12CT13CT14CT15CT16CT17CT18CT1CR2CR3CR4CR5CR6CR7CR8CR9CR10CR11CR12CR13CR14CRIn a right triangle, if the length of the hypotenuse is 5 and the length of one of the other sides is 3, what is the length of the third side? (pp. A14-A15)If is an acute angle, solve the equation tan= 1 2 . Express your answer in degrees, rounded to one decimal place. (p. 475)If is an acute angle, solve the equation sin= 1 2 . (pp.472-475)True or False sin 52 =cos 48The sum of the measures of the two acute angles in a right triangle is ________. (a) 45 (b) 90 (c) 180 (d) 360When you look up at an object, the acute angle measured from the horizontal to a line-of-sight observation of the object is called the ______ _____ ________.True or False In a right triangle, if two sides are known, we can solve the triangle.True or False In a right triangle, if we know the two acute angles, we can solve the triangle.In Problems 9-18, find the exact value of the six trigonometric functions of the angle in each figure.In Problems 9-18, find the exact value of the six trigonometric functions of the angle in each figure.In Problems 9-18, find the exact value of the six trigonometric functions of the angle in each figure.In Problems 9-18, find the exact value of the six trigonometric functions of the angle in each figure.In Problems 9-18, find the exact value of the six trigonometric functions of the angle in each figure.In Problems 9-18, find the exact value of the six trigonometric functions of the angle in each figure.In Problems 9-18, find the exact value of the six trigonometric functions of the angle in each figure.16AYU17AYUIn Problems 9-18, find the exact value of the six trigonometric functions of the angle in each figure.19AYUIn Problems 19-28, find the exact value of each expression. Do not use a calculator. tan 12 cot 7821AYU22AYUIn Problems 19-28, find the exact value of each expression. Do not use a calculator. 1 cos 2 20 cos 2 70In Problems 19-28, find the exact value of each expression. Do not use a calculator. 1+ tan 2 5 csc 2 85In Problems 19-28, find the exact value of each expression. Do not use a calculator. tan 20 cos 70 cos 20In Problems 19-28, find the exact value of each expression. Do not use a calculator. cot 40 sin 50 sin 40In Problems 19-28, find the exact value of each expression. Do not use a calculator. cos 35 sin 55 +sin 35 cos 55In Problems 19-28, find the exact value of each expression. Do not use a calculator. sec 35 csc 55 tan 35 cot 55In Problems 29-42, use the right triangle shown below. Then, using the given information, solve the triangle. b=5 , B= 20 ; find a, c, and AIn Problems 29-42, use the right triangle shown below. Then, using the given information, solve the triangle. b=4 , B= 10 ; find a, c, and AIn Problems 29-42, use the right triangle shown below. Then, using the given information, solve the triangle. a=6 , B= 40 ; find b, c, and AIn Problems 29-42, use the right triangle shown below. Then, using the given information, solve the triangle. a=7 , B= 50 ; find b, c, and AIn Problems 29-42, use the right triangle shown below. Then, using the given information, solve the triangle. b=4 , A= 10 ; find a, c, and BIn Problems 29-42, use the right triangle shown below. Then, using the given information, solve the triangle. b=6 , A= 20 ; find a , c , and BIn Problems 29-42, use the right triangle shown below. Then, using the given information, solve the triangle. a=5 , A= 25 ; find b , c , and BIn Problems 29-42, use the right triangle shown below. Then, using the given information, solve the triangle. a=6 , A= 40 ; find b , c , and BIn Problems 29-42, use the right triangle shown below. Then, using the given information, solve the triangle. c=9 , B= 20 ; find b , a , and AIn Problems 29-42, use the right triangle shown below. Then, using the given information, solve the triangle. c=10 , A= 40 ; find b , a , and BIn Problems 29-42, use the right triangle shown below. Then, using the given information, solve the triangle. a=5 , b=3 ; find c , A and BIn Problems 29-42, use the right triangle shown below. Then, using the given information, solve the triangle. a=2 , b=8 ; find c , A and BIn Problems 29-42, use the right triangle shown below. Then, using the given information, solve the triangle. a=2 , c=5 ; find b , A and BIn Problems 29-42, use the right triangle shown below. Then, using the given information, solve the triangle. b=4 , c=6 ; find a , A and BGeometry The hypotenuse of a right triangle is 5 inches. If one leg is 2 inches, find the degree measure of each angle.Geometry The hypotenuse of a right triangle is 3 feet. If one leg is 1 foot, find the degree measure of each angle.Geometry A right triangle has a hypotenuse of length 8 inches. If one angle is 35 , find the length of each leg.Geometry A right triangle has a hypotenuse of length 10 centimeters. If one angle is 40 , find the length of each leg.Geometry A right triangle contains a 25 angle. (a) If one leg is of length 5 inches, what is the length of the hypotenuse? (b) There are two answers. How is this possible?Geometry A right triangle contains an angle of 8 radian. (a) If one leg is of length 3 meters, what is the length of the hypotenuse? (b) There are two answers. How is this possible?Finding the Width of a Gorge Find the distance from A to C across the gorge illustrated in the figure.Finding the Distance across a Pond Find the distance from A to C across the pond illustrated in the figure.The Eiffel Tower The tallest tower built before the era of television masts, the Eiffel Tower was completed on March 31, 1889. Find the height of the Eiffel Tower (before a television mast was added to the top) using the information given in the illustration.Finding the Distance of a Ship from Shore A person in a small boat, offshore from a vertical cliff known to be 100 feet in height, takes a sighting of the top of the cliff. If the angle of elevation is found to be 25 , how far offshore is the boat?Finding the Distance to a Plateau Suppose that you are headed toward a plateau 50 meters high. If the angle of elevation to the top of the plateau is 20 , how far are you from the base of the plateau?Finding the Reach of a Ladder A 22-foot extension ladder leaning against a building makes a 70 angle with the ground. How far up the building does the ladder touch?Finding the Angle of Elevation of the Sun At 10 AM on April 26, 2009, a building 300 feet high cast a shadow 50 feet long. What was the angle of elevation of the Sun?Directing a Laser Beam A laser beam is to be directed through a small hole in the center of a circle of radius 10 feet. The origin of the beam is 35 feet from the circle (see the figure). At what angle of elevation should the beam be aimed to ensure that it goes through the hole?Finding the Speed of a Truck A state trooper is hidden 30 feet from a highway. One second after a truck passes, the angle between the highway and the line of observation from the patrol car to the truck is measured. See the illustration. (a) If the angle measures 15 , how fast is the truck traveling? Express the answer in feet per second and in miles per hour. (b) If the angle measures 20 , how fast is the truck traveling? Express the answer in feet per second and in miles per hour. (c) If the speed limit is 55 miles per hour and a speeding ticket is issued for speeds of 5 miles per hour or more over the limit, for what angles should the trooper issue a ticket?Security A security camera in a neighborhood bank is mounted on a wall 9 feet above the floor. What angle of depression should be used if the camera is to be directed to a spot 6 feet above the floor and 12 feet from the wall?Parallax One method of measuring the distance from Earth to a star is the parallax method. The idea behind computing this distance is to measure the angle formed between the Earth and the star at two different points in time. Typically, the measurements are taken so that the side opposite the angle is as large as possible. Therefore, the optimal approach is to measure the angle when Earth is on opposite sides of the Sun, as shown in the figure. (a) Proxima Centauri is 4.22 light-years from Earth. If 1 light-year is about 5.9 trillion miles, how many miles is Proxima Centauri from Earth? (b) The mean distance from Earth to the Sun is 93,000,000 miles. What is the parallax of Proxima Centauri?Parallax See Problem 59. 61 Cygni, sometimes called Bessel’s Star (after Friedrich Bessel, who measured the distance from Earth to the star in 1838), is a star in the constellation Cygnus. (a) 61 Cygni is 11.14 light-years from Earth. If 1 light-year is about 5.9 trillion miles, how many miles is 61 Cygni from Earth? (b) The mean distance from Earth to the Sun is 93,000,000 miles. What is the parallax of 61 Cygni?Washington Monument The angle of elevation of the Sun is 35.1 at the instant the shadow cast by the Washington Monument is 789 feet long. Use this information to calculate the height of the monument.Finding the Length of a Mountain Trail A straight trail with an inclination of 17 leads from a hotel at an elevation of 9000 feet to a mountain lake at an elevation of 11,200 feet. What is the length of the trail?Finding the Bearing of an Aircraft A DC-9 aircraft leaves Midway Airport from runway 4 RIGHT, whose bearing is N40E . After flying for 1 2 mile, the pilot requests permission to turn 90 and head toward the southeast. The permission is granted. After the airplane goes 1 mile in this direction, what bearing should the control tower use to locate the aircraft?64AYUNiagara Falls Incline Railway Situated between Portage Road and the Niagara Parkway directly across from the Canadian Horseshoe Falls, the Falls Incline Railway is a funicular that carries passengers up an embankment to Table Rock Observation Point. If the length of the track is 51.8 meters and the angle of inclination is 36 2 , determine the height of the embankment.Willis Tower Willis Tower in Chicago is the second tallest building in the United States and is topped by a high antenna. A surveyor on the ground makes the following measurement: 1. The angle of elevation from his position to the top of the building is 34 . 2. The distance from his position to the top of the building is 2593 feet. 3. The distance from his position to the top of the antenna is 2743 feet. (a) How far away from the (base of the) building is the surveyor located? (b) How tall is the building? (c) What is the angle of elevation from the surveyor to the top of the antenna? (d) How tall is the antenna? Source: Council on Tall Buildings and Urban HabitatConstructing a Highway A highway whose primary directions are north-south is being constructed along the west coast of Florida. Near Naples, a bay obstructs the straight path of the road. Since the cost of a bridge is prohibitive, engineers decide to go around the bay. The illustration shows the path that they decide on and the measurements taken. What is the length of highway needed to go around the bay?Photography A camera is mounted on a tripod 4 feet high at a distance of 10 feet from George, who is 6 feet tall. See the illustration. If the camera lens has angles of depression and elevation of 20 , will George’s feet and head be seen by the lens? If not, how far back will the camera need to be moved to include George’s feet and head?Finding the Distance between Two Objects A blimp, suspended in the air at a height of 500 feet, lies directly over a line from Soldier Field to the Adler Planetarium on Lake Michigan (see the figure). If the angle of depression from the blimp to the stadium is 32 and from the blimp to the planetarium is 23 , find the distance between Soldier Field and the Adler Planetarium.Hot-Air Balloon While taking a ride in a hot-air balloon in Napa Valley, Francisco wonders how high he is. To find out, he chooses a landmark that is to the east of the balloon and measures the angle of depression to be 54 . A few minutes later, after traveling 100 feet east, the angle of depression to the same landmark is determined to be 61 . Use this information to determine the height of the balloon.Mt. Rushmore To measure the height of Lincoln’s caricature on Mt. Rushmore, two sightings 800 feet from the base of the mountain are taken. If the angle of elevation to the bottom of Lincoln’s face is 32 and the angle of elevation to the top is 35 , what is the height of Lincoln’s face?The CN Tower The CN Tower, located in Toronto, Canada, is the tallest structure in the Americas. While visiting Toronto, a tourist wondered what the height of the tower above the top of the Sky Pod is. While standing 4000 feet from the tower, she measured the angle to the top of the Sky Pod to be 20.1 . At this same distance, the angle of elevation to the top of the tower was found to be 24.4 . Use this information to determine the height of the tower above the Sky Pod.Chicago Skyscrapers The angle of inclination from the base of the John Hancock Center to the top of the main structure of the Willis Tower is approximately 10.3 . If the main structure of the Willis Tower is 1451 feet tall, how far apart are the two skyscrapers? Assume the bases of the two buildings are at the same elevation.Estimating the Width of the Mississippi River A tourist at the top of the Gateway Arch (height, 630 feet) in St. Louis, Missouri, observes a boat moored on the Illinois side of the Mississippi River 2070 feet directly across from the Arch. She also observes a boat moored on the Missouri side directly across from the first boat (see diagram). Given that B= cot 1 67 55 , estimate the width of the Mississippi River at the St. Louis riverfront. Source: U.S. Army Corps of EngineersFinding the Pitch of a Roof A carpenter is preparing to put a roof on a garage that is 20 feet by 40 feet by 20 feet. A steel support beam 46 feet in length is positioned in the center of the garage. To support the roof, another beam will be attached to the top of the center beam (see the figure). At what angle of elevation is the new beam? In other words, what is the pitch of the roof?Shooting Free Throws in Basketball The eyes of a basketball player are 6 feet above the floor. The player is at the free-throw line, which is 15 feet from the center of the basket rim (see the figure). What is the angle of elevation from the player’s eyes to the center of the rim? [Hint: The rim is 10 feet above the floor.]Geometry Find the value of the angle in degrees rounded to the nearest tenth of a degree.Surveillance Satellites A surveillance satellite circles Earth at a height of h miles above the surface. Suppose that d is the distance, in miles, on the surface of Earth that can be observed from the satellite. See the illustration on the following page. (a) Find an equation that relates the central angle to the height A. (b) Find an equation that relates the observable distance d and . (c) Find an equation that relates d and h . (d) If d is to be 2500 miles, how high must the satellite orbit above Earth? (e) If the satellite orbits at a height of 300 miles, what distance d on the surface can be observed?Calculating Pool Shots A pool player located at X wants to shoot the white ball off the top cushion and hit the red ball dead center. He knows from physics that the white ball will come off a cushion at the same angle as it hits the cushion. Where on the top cushion should he hit the white ball?One World Trade Center One World Trade Center (1WTC) is the centerpiece of the rebuilding of the World Trade Center in New York City. The tower is 1776 feet tall (including its spire). The angle of elevation from the base of an office building to the tip of the spire is 34 . The angle of elevation from the helipad on the roof of the office building to the tip of the spire is 20 . (a) How far away is the office building from 1WTC? Assume the side of the tower is vertical. Round to the nearest foot. (b) How tall is the office building? Round to the nearest foot.Explain how you would measure the width of the Grand Canyon from a point on its ridge.Explain how you would measure the height of a TV tower that is on the roof of a tall building.The Gibb’s Hill Lighthouse, Southampton, Bermuda In operation since 1846, the Gibb’s Hill Lighthouse stands 117 feet high on a hill 245 feet high, so its beam of light is 362 feet above sea level. A brochure states that ships 40 miles away can see the light and planes flying at 10.000 feet can see it 120 miles away. Verify the accuracy' of these statements. What assumption did the brochure make about the height of the ship?The difference formula for the sine function is sin( AB )= _____ . (p.493)If is an acute angle, solve the equation cos= 3 2 . (pp. 472-475)The two triangles shown are similar. Find the missing length. (pp. A16-A18)If none of the angles of a triangle is a right angle, the triangle is called _____ . a. oblique b. isosceles c. right d. scaleneFor a triangle with sides a, b, c and opposite angles A, B, C, the Law of Sines states that _____ .True or False An oblique triangle in which two sides and an angle are given always results in at least one triangle.True or False The Law of Sines can be used to solve triangles where three sides are known.Triangles for which two sides and the angle opposite one of them are known (SSA) are referred to as the _____ _____ .In Problems 9-16, solve each triangle.In Problems 9-16, solve each triangle.In Problems 9-16, solve each triangle.In Problems 9-16, solve each triangle.In Problems 9-16, solve each triangle.In Problems 9-16, solve each triangle.In Problems 9-16, solve each triangle.In Problems 9-16, solve each triangle.In Problems 17-24, solve each triangle. A= 40 , B= 20 , a=2In Problems 17-24, solve each triangle. A= 50 , C= 20 , a=3In Problems 17-24, solve each triangle. B= 70 , C= 10 , b=5In Problems 17-24, solve each triangle. A= 70 , B= 60 , c=4In Problems 17-24, solve each triangle. A= 110 , C= 30 , c=3In Problems 17-24, solve each triangle. B= 10 , C= 100 , b=2In Problems 17-24, solve each triangle. A= 40 , B= 40 , c=2In Problems 17-24, solve each triangle. B= 20 , C= 70 , a=1In Problems 25-36, two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s). a=3 , b=2 , A= 50In Problems 25-36, two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s). b=4 , c=3 , B= 40In Problems 25-36, two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s). b=5 , c=3 , B= 100In Problems 25-36, two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s). a=2 , c=1 , A= 120In Problems 25-36, two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s). a=4 , b=5 , A= 60In Problems 25-36, two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s). b=2 , c=3 , B= 40In Problems 25-36, two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s). b=4 , c=6 , B= 20In Problems 25-36, two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s). a=3 , b=7 , A= 70In Problems 25-36, two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s). a=2 , c=1 , C= 100In Problems 25-36, two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s). b=4 , c=5 , B= 95In Problems 25-36, two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s). a=2 , c=1 , C= 25In Problems 25-36, two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s). b=4 , c=5 , B= 4037AYU38AYU39AYU40AYU41AYU42AYU43AYU44AYU46AYU47AYU48AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU61AYU62AYU63AYU64AYU