Angles of Elevation and Depression Math

An ant looks up at an angle of elevation of 30 degrees to the top of a tree. If the ant is 40 feet from the base of the tree, what is the height of the tree, to the nearest tenth?

A. 23.1 feet

Frank stands 580 feet from the base of the Statue of Liberty. If the Statue of Liberty is 306 feet tall, what is the angle of depression from the top of the statue's torch to Frank? Round the answer to the nearest tenth.

A. 27.4º

Kendra is flying a kite. The angle of elevation from Kendra to the kite is 56°. If the distance from Kendra's hands to the kite is 50 feet, what is the horizontal distance from Kendra to the point directly under the kite (point B)? Round your answer to the nearest tenth.

A. 28 feet

A 12-foot tree casts a 22-foot shadow. Find the angle of elevation from the tip of the shadow to the top of the tree. Round the answer to the nearest tenth.

A. 28.6°

Kyle is pulled back on a swing so that the rope forms an angle of 30° with the vertical. The distance from the top of the swing set directly to the ground is 12 feet. Find Kyle's height off the ground, x, when he is in the pulled-back position. Round the answer to the nearest hundredth.

A. 3.34 feet

Kyle is pulled back on a swing so that the rope forms an angle of 35° with the vertical. The distance from the top of the swing set directly to the ground is 11 feet. Find Kyle's height off the ground, x, when he is in the pulled-back position. Round the answer to the nearest hundredth.

A. 3.63 feet

Frank stands 450 feet from the base of the Statue of Liberty. If the Statue of Liberty is 306 feet tall, what is the angle of depression from the top of the statue's torch to Frank? Round the answer to the nearest tenth.

A. 33.7°

Amy looks up to the 8-foot basketball hoop as shown. If the vertical distance from the ground to Amy's eyes is 5.9 feet, what is the angle of elevation from Amy to the hoop? Round the answer to the nearest tenth.

A. 5.5º

Carlos is making some observations from the roof of a building. Which angle is the angle of depression from the helicopter to Carlos?

B. angle NMK

An ant looks up to the top of a tree at an angle of elevation of 40 degrees. If the ant is 30 feet from the base of the tree, what is the height of the tree, to the nearest tenth?

C. 25.2 feet

A hiker standing at point G wants to estimate the distance across the lake to point H, which is directly north of her location. She walks 700 feet west to point F. She measures the angle from point F to point H to be 78º north of east. Find the distance across the lake to the nearest tenth of a foot.

C. 3,293.2 feet

Frank stands 500 feet from the base of the Statue of Liberty. If Frank looks up with an angle of elevation of 31 degrees, how tall is the Statue of Liberty, to the nearest foot?

C. 306 feet

The angle of elevation from the tip of the shadow to the top of the tree is 36°. Find the distance from the top of the tree to the tip of the shadow. Round the answer to the nearest tenth.

C. 40.8 feet

From the top of a tree, a bird looks down on a field mouse at an angle of depression of 50°. If the field mouse is 40 meters from the base of the tree, find the vertical distance from the ground to the bird's eyes. Round the answer to the nearest tenth.

C. 47.7 m

Kendra is flying a kite 35 feet in the air. The angle of depression from the kite to where Kendra holds the string is 32 degrees. If Kendra holds the string 3 feet off the ground, what is the distance from her hands to the kite? Round your answer to the nearest tenth.

C. 60.4 feet

A bird at the top of a tree looks down on a field mouse at an angle of depression of 65°. If the field mouse is 30 meters from the base of the tree, find the vertical distance from the ground to the bird's eyes. Round the answer to the nearest tenth.

D. 64.3 m

What is the relationship between the angle of elevation and the angle of depression between two points?

The angle of elevation from one point is congruent to the angle of depression from the other point.