Angle of Elevation – the angle between the line of sight and the horizontal when an observer looks upward

Angle of elevation

Line of sight

The peak of Goose Bay Mountain is 400 meters higher than the end of a local airstrip. The peak rises above a point 2025 meters from the end of the airstrip. A plane takes off from the end of the runway in the direction of the mountain at an angle that is kept constant until the peak has been cleared. If the pilot wants to clear the mountain by 50 meters, what should the angle of elevation be for the takeoff to the nearest tenth of a degree?

2025 m

B

D

C A

50 m

400m

CD = 400 + 50 = 450

tan x° =

tan x° =

x = tan-1 ( )

x ~ 12.5~

x°

Angle of Depression – the angle between the line of sight when an observer looks downward,

and the horizontal.

line of sight

angle of depression

Example: The tailgate of a moving van is 3.5 feet above the ground. A loading ramp is attached to the rear of the van at an incline of 10°. Find the length of the ramp to the nearest tenth foot.

3.5 ft

10°

CB

A

Use Trigonometry to find the length of the ramp (AB).

Example: Olivia is in a light house on a cliff. She observes two sailboats due east of the light house. The angles of depression to the two boats are 33° and 57°

D

C

BA

E

∆CDA and ∆CDB are right triangles, and CD = 110 + 85 or 195. The distance between the boats is AB or BD – AD. Use the right triangles to find these two lengths.

85 ft

110 ft

33°