Transcript L13-1 notes - angles of elevation and depression - fghs

Angle of Elevation – the angle between the line of
sight and the horizontal when an observer looks
upward
Line of sight
Angle of elevation
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?
CD = 400 + 50 = 450
tan x° =
D
tan x° =
50 m
x = tan-1 (
B
)
x ~~ 12.5
400m
C
2025 m
x°
A
Angle of Depression – the angle between the
line of sight when an observer looks downward,
and the horizontal.
angle of depression
line of sight
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.
10°
A
3.5 ft
C
Use Trigonometry to find the length of the ramp (AB).
B
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°
C
E
110 ft
85 ft
33°
D
A
B
∆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.