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If the elevation of the sun is $30^{0}$ , then the length of the shadow cast by a tower of $150$ ft height is ?

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75 \sqrt{3}

ft.

200 \sqrt{3}

ft.

150 \sqrt{3}

ft.

none of these

answer is C.

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Detailed Solution

It is given that the angle of elevation of the sun is

30

° for the shadow of a tower of height

150 ft .

Let the height of the tower

, h = 150 ft

and shadow of the tower,

EC = x

.
We can see that, in

△ AEC,

\tan 30^{o} = \frac{AE}{EC}

… (

\tan 30^{o} = \frac{1}{\sqrt{3}}

).
⇒

\frac{1}{\sqrt{3}} = \frac{h}{x}

⇒

x = h \sqrt{3}

⇒

x = 150 \sqrt{3} ft

Hence, the correct option is 3.

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