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.

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

Example The 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

Angles of Depression An 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

Angle of Depression Line of Sight

Horizontal Line Horizontal Line Angle of Depression Angle of Elevation 55° Angle of Depression Angle of Elevation Horizontal Line 55°

Example You 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. The actual height is 67.4 meters

Lighthouse, Split Rock, Minnesota

Angle of Depression = 33° 195 ft. Lighthouse, Split Rock, Minnesota

33° 195 ft. d

Method 1 Use the alternate interior angle of elevation 195 ft. 33° d 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

Method 2 Use the complementary angle 57° 195 ft. d The angle is 57° The height of the lighthouse is the adjacent side The distance to the boat is the opposite side