Angles of Elevation and Depression

• Solve problems involving angles of elevation

• Solve problems involving angles of depression

Aviators must fly at an angle of elevation to gain enough altitude to get over mountains.

Line of Sight

Angle of Elevation

Angles of ElevationAn Angle of Elevation is the angle between the line of sight and the horizontal when an observer looks upward.

ExampleThe angle of elevation of an airplane is 23°. If the airplane’s altitude is 2500 meters, how far away is it? the distance to the airplane is the

hypotenuse

the altitude of the airplane is the opposite side

591525sin

2500

250025sin

x

x

x

Line of Sight

Angle of Depression

Angles of DepressionAn Angle of Depression is the angle between the line of sight and the horizontal when an observer looks downward.

Angle of Depression

Line of Sight

Horizontal Line

Horizontal Line

55°

55°

Angle of Depression

Angle of Elevation

ExampleYou can walk across the Sydney Harbor Bridge and take a photo of the Opera House from about the same height as top of the highest sail.

This photo was taken from a point about 500 m horizontally from the Opera House and we observe the waterline below the highest sail as having an angle of depression of 8°. How high above sea level is the highest sail of the Opera House?

• The angle of depression is 8°

• The distance to the opera house is the adjacent side.

• The height of the opera house is the opposite side.

h

h

h

27.70

8tan500500

8tan

The actual height is 67.4 meters

Lighthouse, Split Rock, Minnesota

195 ft.

Angle of Depression = 33°

Lighthouse, Split Rock, Minnesota

195 ft.

33°

d

195 ft.

33°

d

Method 1

27.30033tan

195

19533tan

d

d

d

Use the alternate interior angle of elevation

• The angle of elevation/depression is 33°

• The height of the lighthouse is the opposite side

• The distance to the boat is the adjacent side

195 ft.57°

d

Method 2

27.300

57tan195195

57tan

d

d

d

Use the complementary angle

• The angle is 57°

• The height of the lighthouse is the adjacent side

• The distance to the boat is the opposite side