1. 8-5 Angles of Elevation & Depression

2. Angles of Elevation
Angle of Elevation: The angle between the line of sight and the horizontal when an observer looks upward.
Angle of Elevation
Line of Sight

3. Example 1
Find the angle of elevation of the Sun when a 7.6 meters flagpole casts a 18.2 meter shadow. Round to the nearest tenth of a degree.
Tan = Opposite/Adjacent
7.6 m
18.2 m
Tan x = 7.6/18.2
x = tan-1 (7.6/18.2)
x = 22.7°

4. Angle of Depression
Angle of Depression: The angle between the line of sight when an observer looks downward and the horizontal.
Angle of Depression
Line of Sight

5. Example 2
A wheelchair ramp is 3 meters long and inclines at 6°. Find the height of the ramp to the nearest tenth of a centimeter.
Sin = Opposite/Hypotenuse 6° ?
3 m
Sin 6° = x/3
3(Sin 6°) = x
31.4 cm = x

6. Example 3
Two boats are observed by a parasailer 75 meters above a lake. The angles of depression are 12.5° and 7°. How far apart are the boats?
Tan 7° = 75/x1
x1 (Tan 7°) = 75
75 m 7°
12.5°
x1 = 75/Tan 7°
x1 ≈ 610.8
Tan 12.5° = 75/x2
x2 (Tan 12.5°) = 75
x2 = 75/Tan 12.5°
Answer = x1 – x2 = about 273 m
x2 ≈ 338.3

7. Try these p. 466 #1 Answer: about 2.2° #2 Answer: about 169.9 m #3
Answer: C…x = 150/tan12°
Homework #53 p even, 19-21, 27-28