Applying Trigonometric Ratios

The angle of elevation to the top of the Empire State Building in New York is found to be 11 degrees from the ground at a distance of 1 mi from the base of the building. Using this information, find the height of the Empire State Building.

1026 ft

A tree 30 ft high casts a shadow 45 ft long. Find the measure of the angle of elevation of the sun.

33.7 degrees

To estimate the width of a river, Jamie stood directly opposite a large tree on the opposite bank. He then walked 90 ft along the bank and approximated the measure of the angle between is line of sight to the tree and the river's edge to 53. Find the approximate width of the river.

119.4 ft

Ben is flying a kite directly over his buddy Franklin, who is 125 meters away. His kite string makes a 39 degree angle with the level ground. To the nearest meter, how long is the kite string?

161 m

A guy wire stretches from the ground to the top of a 1,500 ft TV tower. If the wire makes an angle measuring 63 with the ground, how long is the wire?

1683 ft

With the sun at an angle of elevation of 50 degrees (looking up to the sun), the shadow of a tree is 15 m long. Find the height of the tree to the nearest meter.

18 m

A 20-ft ladder leans against a building so that the angle between the ground and the ladder is 72 degrees. How high does the ladder reach on the building?

19 ft

From the top of a cliff 160 ft high, a bird sees a worm on a rock. The bird's angle of depression to the worm on the rock is 52 degrees. How far, to the nearest foot, must the bird fly to get the worm?

203 ft

A man is standing 75 ft from the base of a cliff. The angle of elevation to the top of the cliff is 70. How high is the cliff?

206 ft

A 24 ft ladder positioned against a wall forms an angle of 75 degrees with the ground. How high up the wall does the ladder reach? How far is the base of the ladder from the wall?

23.2 ft; 6.2 ft

The angle of elevation from a point 49 meters from the base of a flagpole to the top is 27 degrees. Find the height of the flagpole.

25 m

A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level, and estimates the angle of elevation of the kite to be 50 degrees. If the string is 450 ft long, how high is the kite above the ground?

345 ft

When Mario stands 240 ft from the base of a sequoia tree, he is 360 ft from the top of the tree. Find the measure of the angle of elevation of to the top of the tree.

48 degrees

A woman wants to use a 10 ft ladder to get to a window 8 ft above the ground. At what angle does the ladder need to be set?

53 degree

A flagpole is 28 ft high and the distance along the line of sight from the top of the flagpole to a person at a distance from its base is 35. What is the angle of depression from the top of the flagpole to the person?

53.1 degrees

An eagle is flying level with the top of a cliff and 600 ft away from the cliff. The eagle spots a field mouse at the base of the cliff. The measure of the angle of depression is 42. How high is the cliff?

540 ft

The length of a kite string is 900 ft. If the measure of the angle of elevation of the kite is 38, find the height of the kite above the ground.

554 ft

A person standing 800 ft from the base of the Washington Monument finds that the measure of the angle of elevation of the top of the monument is 35. How tall is the Washington Monument?

560 ft

Air-traffic controller Seymour Flytz must calculate the angle of descent (depression) for an incoming jet. The jet's land distance is 44 km from the control tower and the plane is flying at an altitude of 5.6 km. Find the angle of descent.

7.3 degrees

A 20-ft ladder is leaning against a building. If the base of the ladder is 6 ft from the base of the building, what is the angle of elevation of the ladder? How high does the ladder reach on the building?

72.5 degrees, 19 ft