Download 05 Angles of Elevation and Depression

Mathematics
Stage 5.2
Elevation and
Depression.
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Elevation & Depression (1/5)
Up
Elevation
θ
θ
Depression
Down
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Angle of Elevation (2/5)
A boat is 100 m from a lighthouse.
The height og the Lighthouse is 6 m.
What is the lighthouse’s angle of elevation?
6
100
θo = tan-1 (6 ÷ 100)
θo = 3.4336o
θo = 3.4o m
tan θo =
6m
θo
100m
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Angle of Depression (3/5)
An aero plane is 1 km from a runway.
It is at a height of 300 m.
What is the planes angle of depression?
1,000m
θO
300 m
300
Tan θ = 1000
θo = tan-1 (0.3)
θo = 16.6992442o
θo = 17o
o
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Angle of Elevation (4/5)
A boat is 100m from a lighthouse.
o
It has an angle of elevation of 30 .
What is the height of the lighthouse? (h)
h
100
h = 100 x Tan 30o
h = 57.735 026 919
h = 57.7 m
tan 30o =
h
30o
100m
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Angle of Depression (5/5)
An aero plane is 3 km from a runway.
The angle of depression is 15o.
What is the altitude of the plane?
3 km
15O
a
a
tan 15 = 3
a = 3 x Tan 15o
a = 0.803 84 km
a = 804 m
o
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