7.5 Angles of Elevation and Depression

Angle of Elevation• The angle between the line of sight

and the horizontal when an observer looks upward.

Line of Sight

Horizontal

Example 1• Little Suzie let go of her balloon. It floated to the

top of the gym, 50 feet above the ground. Her big brother Matthew is standing 60 feet away. What is the angle of elevation from him to the balloon?

60 ft

50 ft

xo6050tan x

AdjacentOppositeTangent

40x

Example 2• Find the angle of elevation of the sun

when a 7.6 meter flagpole casts an 18.2 m shadow. Round to the nearest tenth.

2.186.7tan x

AdjacentOppositeTangent

7.22x

7.6 m

18.2 m

xo

Class work 7.5 – SG&I P85 ALL

Angle of Depression• The angle between the line of sight

and the horizontal when an observer looks downward.

Horizontal

Line of SightAll “angle of

depression” problems will require you to re-draw the triangle!!!

Example 1• A hiker is standing on the top of a 100

yard cliff. He is looking down at a cabin on the ground below him. The cabin is 230 yards from the base of the cliff. What is the angle of depression?

230 yd

100 yd

xtan230100tan x

100 yd

230 yd

x23x

Example 2• A sledding run is 300 yards long with a

vertical drop of 27.6 yards. Find the angle of depression of the run.

x

5x

3006.27sin x

27.6 yd27.6 yd 300 yd

Example 3• A salvage ship uses sonar to determine

that the angle of depression to a wreck on the ocean floor is 13o. The depth chart shows that the ocean floor is 40 meters below the surface. How far must a diver lowered from the ship walk along the ocean floor to reach the wreck?

13

13tan40

x

x4013tan

3.173x

40 m 40 m

x

x

Class work 7.5 – SG&I P86 ALL