A communications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 61°. A guy wire is to be attached to the top of the tower and to the ground, 136 yd downhill from the base of the tower. The angle formed by the guy wire is 21°. Find the length of the cable required for the guy wire. 21° 136 yd 61°

Q: A ship's sonar finds that the angle of depression to a wreck on the bottom of the ocean is 12.5º. If…

A: Here, A is the position of ship's sonar and C is the position of wreck. We need to calculate the…

Q: Two tugboats that are a = 150 ft apart pull a barge, as shown. If the length of one cable is b = 216…

A: Use cosine formula.

Q: A radio tower is located 425 feet from a building. From a window in the building, a person…

A:

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

A:

Q: A kite is flying 95 ft off the ground, and its string is pulled taut. The angle of elevation of the…

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Q: A radio tower is located 275 ft from a building. from a window in the building, a person determines…

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Q: A boat is 1000 meters from the base of a cliff. If the angle of depression from the top of the cliff…

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Q: To the nearest degree, what is the angle of depression from the hawk to the rabbit? 34° O 40° O 50°…

A: Let the angle of depression be X

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 radio tower is located 300 feet from a building. From a window in the building, a person…

A:

Q: An aerial photographer who photographs real estate properties has determined that the best photo is…

A: Form the right triangle and use the trigonometric ratios.

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 radio tower is located 400 feet from a building. From a window in the building, a person…

A: for the upper triangle, use the tan function  tan36=x400 x=400tan36 x=400·0.7265425 x=290.61701

Q: A is located 250 ft from a building. From a window in the building, a person determines that the…

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: A 18-ft ladder leans against a building so that the angle between the ground and the ladder is 74°.…

A:

Q: A kite is flying at an angle of elevation of 67° with the ground. If 100 ft of string have been paid…

A: Since, it is given that a kite is flying at an angle of elevation of 67° withthe ground.∠B=67°Since,…

Q: A ship is on the surface of the water, and its radar detects a submarine at a distance of 238 ft, at…

A: Here we have to use basic trigonometric ratios to find the depth of the submarine.

Q: A building 210 feet tall casts a 60 foot long shadow. If a person looks down from the top of the…

A:

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: From the top of a 190-ft lighthouse, the angle of depression to a ship in the ocean is 21°. How far…

A: Given that height of lighthouse is 190 ft. And depression angle is 21°. And we find that how far is…

Q: Two tugboats that are a = 130 ft apart pull a barge, as shown. If the length of one cable is b = 202…

A:

Q: A ship starts at point X, travels 200 miles to point Y, adjusts its route according to the angle…

A: *to find:- xz.

Q: Find the height of a clock tower if the angle of elevation from a horizontal point 430 m from its…

A:

Q: The angle of elevation from a viewer to the center of a fireworks display is 55°, If the viewer is…

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Q: A radio transmission tower is 130 feet tall. How long should a guy wire be if it is to be attached…

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

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Q: The horizontal distance on a survev map from the top edge of a riverbank to the river is 85 feet…

A:

Q: A 19-ft ladder leans against a building so that the angle between the ground and the ladder is 65°.…

A: Given: A 19-ft ladder leans against a building so that the angle between the ground and the ladder…

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: A surveyor starts at the edge of a lake, at point 4, and measures a 90° angle between B and C, as…

A: The solution as follows :-

Q: To find the distance from the house at A to the house at B, a surveyor measures the angle ACB, which…

A: Given Data: The measure of angle C is: m∠C=10° The distance between A and C is: AC=50 ft The…

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: An airship is flying at an altitude of 800 m when it spots a village in the distance with a…

A: Consider the diagram given below, Point A is the location of the plane at that instant, point C is…

Q: From the top of a 200-ft lighthouse, the angle of depression to a ship in the ocean is 29°. How far…

A:

Q: Two tugboats that are a = 105 ft apart pull a barge, as shown. If the length of one cable is b = 214…

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: Two boats are traveling toward a lighthouse that is 200 feet (ft) above sea level at its top. When…

A:

Q: 1) From the top of a coconut tree is 20m tall. A dog is spotted at an angle of depression of 15°.…

A:

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 from the house at A to the house at B, a surveyor measures the angle ACB, which…

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: From the top of a 200 foot lighthouse, the angle of depression to a ship in the ocean is 13°. How…

A: Answer and explanation is given below..

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

A:

Q: The base of the ladder in the figure is a 7 ft from the building, and the angle formed by the ladder…

A:

Q: From the top of a 220-ft lighthouse, the angle of depression to a ship in the ocean is 28°. How far…

A:

Q: A straight kite string makes an angle of 40° with the ground, as shown in the diagram. If y = 240…

A: y=240 ft θ=40o from right angle triangle sinθ=perpendicularhypotenuse

Q: What is the angle of depression from the plane to the​ building?(Round to the nearest degree as​…

A:

Q: A person 100 meters from the base of a tree, observes that the angle between the ground and the top…

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.