Suppose that from atop of 100m vertical cliff a ship is spotted at an angle of depression of 12 degrees. How far is the ship from the base of the cliff?
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Step-by-step explanation:
The height of the lighthouse AB=120 metres. The observer is at A.
The ship at D makes an angle of depression 30
o
and the ship at C makes an angles of depression 60
o
.
Taking DC=y and CB=x
In right angled ΔACB
tan60
o
=
CB
AB
∴
3
=
x
120
∴x=
3
120
×
3
3
(Rationalizing)
∴ =
3
120
3
=40
3
In right angled ΔADB
tan30
o
=
BD
AB
3
1
=
x+y
120
x+y=120
3
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