Angle of Elevation and Depression

Problems for Angle of Elevation
Problems:
1. A ladder with its foot on a horizontal flat surface rests against a wall. It makes an angle of 30° with the horizontal. The foot of the ladder is 41 ft from the base of the wall. Find the height of the point where the ladder touches the wall.
Solution:
Draw the figure for the given data.

[Given]
The distance from the foot of the ladder to the foot of the wall adjacent = 41 ft, and the angle of elevation is 30°
Leto be the height of the side at which the ladder touches the wall.

[Solution]
Tan30°=

the ladder touches the wall at a height of 23.67 ft. 2. The angle of elevation of the top of a tree is 30o from a point 28 ft away from the foot of the tree. Find the height of the tree rounded to the nearest feet.
[Given]
The measure of the angle of elevation from point A is 30.
The adjacent side was 28ft
[Solution]

So, the height of the tree is 16.17 ft.

3. A building is 50 feet high. At a distance away from the building, an observer notices that the angle of elevation to the top of the building is 41º. How far is the observer from the base of the building?

[Given]
The opposite side was 50ft
The angle of elevation was 41°

[Solution] The distance of the observer to the base of the building.

4. Gwen wants to measure the height of a tree. She walks exactly 100 feet from the base of the tree and looks up. The angle of elevation from the ground to the top of the tree is 45º . How tall is the tree?

[Given]
The adjacent side was 100ft
The angle of elevation was 45°

[Solution] The height of the tree is 100ft.

5. Calculate the angle of elevation of the line of sight of a person whose eye is 1.7 above the ground, and is looking at the top of a flagpole which is 27.5 m away on level ground and 18.6 m high.
[Solution]
Note that the right triangle for which the line of sight forms the hypotenuse is 16.9 m high after we take into account the 1.7 m distance that