A communications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 64°. A guy wire is to be attached to the top of the tower and to the ground, 113 ft downhill from the base of the tower. The angle formed by the guy wire is 10°. Find the length of the cable required for the guy wire. 10° 113 ft 64°

Q: After a hurricane, a homeowner examines a tree on his property for damage. He thinks a 20-ft palm…

A: A homeowner examines trees on his property for damage. A 20 foot palm tree is leaning slightly from…

Q: The angle of elevation of a pedestrian crosswalk over a busy highway is 9.34°​,as shown in the…

A: The solution is:

Q: from a hot air balloon 2 km high, a person look east sees one town with angle of depression of 12…

A:

Q: From a window 30 feet above the level ground, a building 100 feet high, and at a distance of 200…

A:

Q: E. From the top of a 250 ft lighthouse, then angle of depression to a ship in the ocean is 18. How…

A:

Q: At a point 200 feet from the base of a building, the angle of elevation to the bottom of a…

A:

Q: An observer is 120 ft from the base of a television tower, which is 150 ft tall. Find the angle of…

A: Given query is to find the angle of elevation.

Q: A boy is 1.5 m tall standing 12 m away from a church building which has a tower on top of its roof.…

A: We are given that a boy is 1.5 m tall standing 12 m away from a church building that has a tower on…

Q: A pilot is at an altitude of 3,000 ft, and is 7,060 ft in horizontal distance from the end of the…

A:

Q: A surveyor starts at the edge of a lake, at point A, and measures a 90° angle between B and C, as…

A: Here we will find the length of the lake between A and C,

Q: A surveyor wishing to find the height of a lighthouse measures the angle A at a point 120 ft. from…

A: Let the height of the light of the lighthouse is h. See the picture below

Q: A hunter is laying on the ground near a 15 foot tall tree. He sees his prey on top of the tree at an…

A:

Q: A campsite is 8.51 miles from a point directly below the mountain top. If the angle of elevation is…

A:

Q: The 150-foot-long string of a kite you are flying is being pulled taut by the wind and makes an…

A:

Q: At the Denver International Airport, planes must clear a mountain that is 1000 feet tall that is a…

A: We have to find angle of elevation must the plane take off in order to safely clear the mountain

Q: Two tugboats that are a = 110 ft apart pull a barge, as shown. If the length of one cable is b = 202…

A: Given that We have to evaluate the angle formed by two cables

Q: 7) Find the height of a building that projects a shadow of 350 ft on the ground, if the angle of…

A: The height of the building that projects a shadow of 350 ft on the ground  and the angle of…

Q: The angle of elevation to the top of a building in Seattle is found to be 2.8 degrees from the…

A: Given that: Angle of elevation  = 2.8°Distance from the base = 1.5 miles

Q: Determine value of angle a to the nearest tenth of a degree

A: Given that  sin α=13 in the interval π2<α<π cos β=-13in the interval π<β<3π2

Q: The angle of elevation to the top of a Building in New York is found to be 5 degrees from the ground…

A: From the given information, Angle of elevation of a Building from ground, θ=50 Distance from the…

Q: If a loading ramp is placed next to a truck, at a height of 2 feet, and the ramp is 20 feet long,…

A:

Q: Consider the following figure: Transit 27.8° 131 ft 5.5 ft From a transit station located 5.5 ft…

A: By trigonometric Identity we solve the following problem

Q: The Willis Tower in Chicago is 1454 feet tall and is situated about 1 mile inland from the shore of…

A:

Q: a1. The angle of depression from a bird sitting on top of a telephone pole to the base of a tree 12…

A: we are given with word problem.

Q: 1. From the top of a cliff 400 feet above sea level, the angle of depression of a boat out to sea is…

A:

Q: A building 290 feet tall casts a 100 foot long shadow. If a person stands at the end of the shadow…

A: Given, Building’s height = 290 feet Shadow’s length = 100 feet Person’s height = 5 feet

Q: The angle of elevation to the top of a Building in New York is found to be 3 degrees from the ground…

A: Consider the below figure

Q: A ladder 5 m long leans against a building. If the angle between the ground and the ladder is 57…

A: Given: according to given data figure will be Where; AC is length of ladder, BC is distance between…

Q: The shadow of a red-pine tree in Northern Minnesota is 131 feet long when the angle of depression…

A: Given: The red-pine tree AB with its shadow BC = 131 ft. The angle of depression is 31o.

Q: A satellite orbiting the earth passes directly overhead at observation stations in Phoenix and Los…

A:

Q: A person in a small boat, offshore from a vertical cliff known to be 100 feet in height, takes a…

A:

Q: . The Sears Tower in Chicago is 1454 feet tall and is situated about 1 mile inland from the shore of…

A:

Q: A lamppost casts a shadow of 18 ft when the angle of elevation of the Sun us 33.7 degrees. How high…

A: Sketch the situation roughly.Let the height of the lamp post is h ft

Q: A surveyor set up his instrument at A and measured the angle of elevation of the top of a tower and…

A:

Q: person standing 397 feet from the base of a church observed the angle of elevation to the church's…

A: A person standing 397 feet from the base of a church observed the angle of elevation to the church's…

Q: A 16 foot ladder leaning against a wall of a house makes a 50∘angle with the ground. How far up the…

A:

Q: A 35-foot ladder is leaning against the side of a building. If the ladder makes an angle of 24o 10'…

A: Given:A 35-foot ladder is leaning against the side of a building and it makes an angle of 24 degree…

Q: A person standing 100 feet from the bottom of a cliff notices a tower on top of the cliff. The angle…

A: Given that  A person standing 100 feet from the bottom of a cliff. The angle of elevation of the top…

Q: From the top of a fire tower that is 45 feet high, a forest ranger sees her colleague on the ground…

A: From the top of a fire tower that is 45 feet high, a forest ranger sees her colleague on the ground…

Q: A ship is just off the shore of New York City. A sighting is taken on the Statue of Liberty, which…

A: Given  Height = 305 feet  Base = 950 feet  We need to find the angle of elevation

Q: To find the distance between two small towns, an electronic distance measuring (EDM) instrument is…

A:

Q: A 16 foot ladder is used to scale a 14.5 foot wall. At what angle of elevation must the ladder be…

A: Please see the answer below.

Q: A 7-ft ladder leans against the side of a house. How far is the bottom of the ladder from the side…

A: Angle of elevation of ladder =64∘ Here we will apply cosine formula which is given as-…

Q: At an altitude of 3,500 ft, the engine on a small plane fails. What angle of depression is needed to…

A:

Q: From a distance of 300 m, Susan looks up at the top of a lighthouse. The angle of elevation is 5°.…

A: Given, From a distance of 300 m, Susan looks up at the top of a lighthouse. The angle of elevation…

Q: 1. A 20-foot ladder leans against a wall so tha the base of the ladder is 8 feet from the base of…

A: Given :- Length of ladder=20 ftBase of ladder is 8 ft from the base of building .We have to find…

Q: A mountain cabin is built on the side of a hill with a porch extending over a portion of the…

A: The diagram is shown below:

Q: Find the measure of the indicated angle to the nearest degree

A:

Q: 6. From the top of Mt. Banahaw 135m high, it is observed that the angle of depression of a ship is…

A:

Q: Find the value of the marked angle to the nearest degree. 27 11 1?

A:

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.