Question

Matt is standing on top of a cliff 305 feet above a lake. The measurement of the angle of depression to a boat on the lake is 42 degree. How far is the base of the cliff?

Answer 1

Given that,

Height of the cliff, h = 305 ft

Angle of depression is 42 degree.

To find,

The distance between boat and Matt.

Solution,

Let x is the distance between boat and Matt. Using trigonometry to find it.

$\tan\theta=\dfrac{305}{x}\\\\x=\dfrac{305}{\tan\theta}\\\\x=\dfrac{305}{\tan(42)}\\\\x=338.73\ m$

So, the base is 338.73 m away form the cliff.

Learn more,

Height and distance

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