8-58-5 Angles of Angles of Elevation & DepressionElevation & Depression

Angles of ElevationAngles of Elevation

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

Angle of Elevation

Line of Sight

Example 1Example 1 Find the angle of elevation of the Sun Find the angle of elevation of the Sun

when a 7.6 meters flagpole casts a 18.2 when a 7.6 meters flagpole casts a 18.2 meter shadow. Round to the nearest meter shadow. Round to the nearest tenth of a degree.tenth of a degree.

7.6 m

18.2 m

Tan = Opposite/Adjacent

Tan x = 7.6/18.2

x = tan-1 (7.6/18.2)

x = 22.7°

Angle of DepressionAngle of Depression

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

Angle of Depression

Line of Sight

Example 2Example 2

A wheelchair ramp is 3 meters long and A wheelchair ramp is 3 meters long and inclines at 6°. Find the height of the ramp inclines at 6°. Find the height of the ramp to the nearest tenth of a centimeter.to the nearest tenth of a centimeter.

6°?

3 m

Sin = Opposite/Hypotenuse

Sin 6° = x/3

3(Sin 6°) = x

31.4 cm = x

Example 3Example 3

Two boats are observed by a parasailer 75 Two boats are observed by a parasailer 75 meters above a lake. The angles of meters above a lake. The angles of depression are 12.5° and 7°. How far depression are 12.5° and 7°. How far apart are the boats?apart are the boats?

Tan 7° = 75/x1

75 m

7°12.5°

7°12.5°

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 Answer = x1 – x2 = about 273 m

Try theseTry these

p. 466 #1p. 466 #1 Answer: about 2.2°Answer: about 2.2° #2#2 Answer: about 169.9 mAnswer: about 169.9 m #3#3 Answer: C…x = 150/tan12°Answer: C…x = 150/tan12° Homework #53 p. 467 4-18 even, 19-Homework #53 p. 467 4-18 even, 19-

21, 27-2821, 27-28