1. Depression and Elevation
If a person on the ground looks up to the top of a building, the angle formed between the line of sight and the horizontal is called the angle of elevation.
If a person standing on the top of a building looks down at a car on the ground, the angle formed between the line of sight and the horizontal is called the angle of depression.
horizontal
angle of depression
line of sight
angle of elevation
horizontal

2. 1. From a point 80m from the base of a tower, the angle of elevation is 28˚. How tall is the tower?x
28˚ 80
Using the 28˚ angle as a reference, we know opposite and adjacent sides.
Use
tan
tan 28˚ =
80 (tan 28˚) = x
80 (.5317) = x
x ≈ 42.5
About 43 m

3. 2. A ladder that is 20 ft is leaning against the side of a building
2. A ladder that is 20 ft is leaning against the side of a building. If the angle formed between the ladder and ground is 75˚, how far is the bottom of the ladder from the base of the building? 20
building
ladder
75˚ x
Using the 75˚ angle as a reference, we know hypotenuse and adjacent side.
Use
cos
cos 75˚ =
20 (cos 75˚) = x
20 (.2588) = x
x ≈ 5.2
About 5 ft.

4. 6. The angle of depression from the top of a tower to a boulder on the ground is 38º. If the tower is 25m high, how far from the base of the tower is the boulder?
38º
angle of depression 25
Alternate Interior Angles are congruent
38º x
Using the 38˚ angle as a reference, we know opposite and adjacent side.
Use
tan
tan 38˚ = 25/x
(.7813) = 25/x
X = 25/.7813
x ≈ 32.0
About 32 m