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8-5 Angles of Elevation & Depression - PowerPoint PPT Presentation

8-5 Angles of Elevation & Depression. Line of Sight. Angle of Elevation. Angles 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. Example 1.

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8-5 Angles of Elevation & Depression

Angle of Elevation

Angles of Elevation

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

18.2 m

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 x = 7.6/18.2

x = tan-1 (7.6/18.2)

x = 22.7°

Line of Sight

Angle of Depression

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

?

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

Sin 6° = x/3

3(Sin 6°) = x

31.4 cm = x

12.5°

75 m

12.5°

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

x1 = 75/Tan 7°

x1 ≈ 610.8

Tan 12.5° = 75/x2

x2 (Tan 12.5°) = 75

x2 = 75/Tan 12.5°

x2 ≈ 338.3

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