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8-5Angles of Elevation & Depression

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8-5Angles of Elevation & Depression

Line of Sight

Angle of Elevation

- Angle of Elevation: The angle between the line of sight and the horizontal when an observer looks upward.

7.6 m

18.2 m

- 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

Tan x = 7.6/18.2

x = tan-1 (7.6/18.2)

x = 22.7°

Angle of Depression

Line of Sight

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

3 m

?

6°

- 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

Sin 6° = x/3

3(Sin 6°) = x

31.4 cm = x

7°

12.5°

75 m

7°

12.5°

- 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

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

- p. 466 #1
- Answer: about 2.2°
- #2
- Answer: about 169.9 m
- #3
- Answer: C…x = 150/tan12°
- Homework #54 p. 467 4-18 even, 19-21, 27-28