Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus
15CT16CT17CT18CT1CR2CR3CR4CR5CR6CR7CRGraph each of the following functions :
Solve the triangle for which side a is 20, side c is 15, and angle C is 40.10CR11CR12CR13CRSuppose that f(x)=4x+5 and g(x)=x2+5x24. Solve f(x)=0. Solve f(x)=13. Solve f(x)=g(x). Solve f(x)0. Solve g(x)0. Graph y=f(x). Graph y=g(x).In 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 485AYUWhen 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 ______ _____ ________.7AYU8AYUIn 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.16AYUIn Problems 9-18, find the exact value of the six trigonometric functions of the angle in each figure.18AYUIn Problems 19-28, find the exact value of each expression. Do not use a calculator. sin 38 cos 52In Problems 19-28, find the exact value of each expression. Do not use a calculator. tan 12 cot 78In Problems 19-28, find the exact value of each expression. Do not use a calculator. cos 10 sin 8022AYUIn 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 A32AYUIn 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 B34AYU35AYUIn 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 A38AYUIn 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 B41AYU42AYUGeometry 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 26,2019, 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 measurements : The angle of elevation from his position to the top of the building is 34. The distance from his position to the top of building is 2595 feet. The distance from his position to the top of antenna is 2760 feet. How far away from the (base of the) building is the surveyor located ? How tall is the building ? What is the angle of elevation from the surveyor to the top of the antenna ? How tall is the antenna ?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?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 that at which is hit the cushion. If the deflection angle, , is 52, where on the top cushion should he hit the white ball ?80AYU81AYU82AYU83AYU84AYUThe difference formula for the sine function is sin( AB )= _____ . (p.493)2AYU3AYU4AYU5AYU6AYU7AYU8AYUIn 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 , solve each triangle.
In Problems 17-24, solve each triangle. A= 50 , C= 20 , a=3In Problems 1926, solve each triangle. B=64,C=47,b=6In 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 2738, 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=9,c=4,B=115In 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 , 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).
In 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 , 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).
In 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 2738, 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=7,c=3,C=12In 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= 4037AYU38AYUFinding the Length of a Ski Lift Consult the figure. To find the length of the span of a proposed ski lift from P to Q , a surveyor measures DPQ to be 25 and then walks back a distance of 1000 feet to R and measures PRQ to be 15 . What is the distance from P to Q ?Finding the Height of a Mountain Use the illustration in Problem 37 to find the height QD of the mountain.Finding the Height of an Airplane An aircraft is spotted by two observers who are 1000 feet apart. As the airplane passes over the line joining them, each observer takes a sighting of the angle of elevation to the plane, as indicated in the figure. How high is the airplane?Finding the Height of the Bridge over the Royal Gorge The highest bridge in the world is the bridge over the Royal Gorge of the Arkansas River in Colorado. Sightings to the same point at water level directly under the bridge are taken from each side of the 880-foot-long bridge, as indicated in the figure. How high is the bridge? Source: Guinness Book of World Records43AYU44AYU45AYU46AYU47AYU48AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU61AYU62AYUMake up three problems involving oblique triangles. One should result in one triangle, the second in two triangles, and the third in no triangle.64AYUWhat do you do first if you are asked to solve a triangle and are given two sides and the angle opposite one of them?Write the formula for the distance d from P 1 =( x 1 , y 1 ) to P 2 =( x 2 , y 2 ) . (p. 4)If is an acute angle, solve the equation cos= 2 2 .(pp.472—475)If three sides of a triangle are given, the Law of ________ is used to solve the triangle.4AYU5AYUTrue or False Given only the three sides of a triangle. there is insufficient information to solve the triangle.True or False The Law of Cosines states that the square of one side of a triangle equals the sum of the squares of the other two sides, minus twice their product.True or False A special case of the Law of Cosines is the Pythagorean Theorem.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 17-32, solve each triangle. a=3 , b=4 , c =40In Problems 17-32, solve each triangle. a=2 , c=1 , B =10In Problems 1732, solve each triangle. b=2,c=4,A=75In Problems 17-32, solve each triangle. a=6 , b=4 , C =60In Problems solve each triangle.
In Problems 17-32, solve each triangle. b=4 , c=1 , A =120In Problems solve each triangle.
In Problems 17-32, solve each triangle. a=3 , c=2 , B =90In Problems solve each triangle.
In Problems 17-32, solve each triangle. a=4 , b=5 , c=3In Problems 17-32, solve each triangle. a=2 , b=2 , c=2In Problems 17-32, solve each triangle. a=3 , b=3 , c=2In Problems 1732, solve each triangle. a=6,b=11,c=12In Problems 17-32, solve each triangle. a=4 , b=3 , c=6In Problems 17-32, solve each triangle. a=10 , b=8 , c=5In Problems 17-32, solve each triangle. a=9 , b=7 , c=10In Problems 33-42, solve each triangle using either the Law of Sines or the Law of Cosines. B =20 , C =75 , b=5In Problems 33-42, solve each triangle using either the Law of Sines or the Law of Cosines. A =50 , B =55 , c=9In Problems 33-42, solve each triangle using either the Law of Sines or the Law of Cosines. a=6 , b=8 , c=936AYU37AYUIn Problems 33-42, solve each triangle using either the Law of Sines or the Law of Cosines. a=4 , C=5 , B =5539AYU40AYU41AYU42AYUDistance to the Green A golfer hits an errant tee shot that lands in the rough. A marker in the center of the fairway is 150 yards from the center of the green. While standing on the marker and facing the green, the golfer turns 110 toward his ball. He then paces off 35 yards to his ball. See the figure. How far is the ball from the center of the green?Navigation An airplane flies due north from Ft. Myers to Sarasota, a distance of 150 miles, and then turns through an angle of 50 and flies to Orlando, a distance of 100 miles. See the figure. a. How far is it directly from Ft. Myers to Orlando? b. What bearing should the pilot use to fly directly fron Ft. Myers to Orlando?Avoiding a Tropical Storm A cruise ship maintains an average speed of 15 knots in going from San Juan, Puerto Rico, to Barbados, West Indies, a distance of 600 nautical miles. To avoid a tropical storm, the captain heads out of San Juan in a direction of 20 off a direct heading to Barbados. The captain maintains the 15-knot speed for 10 hours, after which time the path to Barbados becomes clear of storms. a. Through what angle should the captain turn to head directly to Barbados? b. Once the turn is made, how long will it be before the ship reaches Barbados if the same 15-knot speed is maintained?Revising a Flight Plan In attempting to fly from Chicago to Louisville, a distance of 330 miles, a pilot inadvertently took a course that was 10 in error, as indicated in the figure. a. If the aircraft maintains an average speed of 220 miles per hour, and if the error in direction is discovered after 15 minutes, through what angle should the pilot turn to head toward Louisville? b. What new average speed should the pilot maintain so that the total time of the trip is 90 minutes?Major League Baseball Field A major league baseball diamond is actually a square 90 feet on a side. The pitching rubber is located 60.5 feet from home plate on a line joining home plate and second base. a. How far is it from the pitching rubber to first base? b. How far is it from the pitching rubber to second base? c. If a pitcher faces home plate, through what angle does he need to turn to face first base?Little League Baseball Field According to Little League baseball official regulations, the diamond is a square 60 feet on a side. The pitching rubber is located 46 feet from home plate on a line joining home plate and second base. a. How far is it from the pitching rubber to first base? b. How far is it from the pitching rubber to second base? c. If a pitcher faces home plate, through what angle does he need to turn to face first base?Finding the Length of a Guy Wire The height of a radi tower is 500 feet, and the ground on one side of the tower slopes upward at an angle of 10 (see the figure). a. How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the slope side 100 feet from the base of the tower? b. How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a positio 100 feet from the baseon the flat side?Finding the Length of a Guy Wire A radio tower 500 feet high is located on the side of a hill with an inclination to the horizontal of 5 . See the figure. How long should two guy wires be if they are to connect to the top of the tower and be secured at two points 100 feet directly above and directly below the base of the tower?51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU61AYU62AYU63AYUThe area K of a triangle whose base is b and whose height is h is _______. (p. A15)If two sides a and b and the included angle C are known in a triangle, then the area K is found using the formula K= .The area K of a triangle with sides a , b , and c is K= , where s= .4AYU5AYU6AYU7AYU8AYU9AYU10AYU11AYU12AYU13AYU14AYU15AYU16AYU17AYU18AYU19AYU20AYU21AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYU29AYU30AYU31AYU32AYU33AYU34AYUCost of a Triangular Lot The dimensions of a triangular lot are 100 feet by 50 feet by 75 feet. If the price of such land is 3 per square foot, how much does the lot cost?36AYU37AYU38AYU39AYU40AYU41AYU42AYU43AYU44AYU45AYU46AYU47AYU48AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYUThe amplitude A and period T of f( x )=5sin( 4x ) are __ and ___. (pp. 412—414)2AYU3AYU4AYU5AYU6AYU7AYU8AYURework Problem 7 under the same conditions, except that at time t=0, the object is at its rest position and moving down. a=5;T=2 seconds10AYURework Problem 9 under the same conditions, except that at time t=0, the object is at its rest position and moving down. a=7;T=5 secondsRework Problem 10 under the same conditions, except that at time the object is at its rest position and moving down.
seconds
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