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Find the length of the shadow cast by 50 m high building, when the angle of elevation of the sun is $30^{\circ}$ .

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\frac{50}{\sqrt{3}} m

50 \sqrt{3} m

25 \sqrt{3} m

100 \sqrt{3} m

answer is B.

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Detailed Solution

Given that height of building is 50 m and angle of elevation of the sun is

30^{\circ}

Let the shadow's length be x m.

.

△ ACB,

\tan 30^{\circ} = \frac{AB}{BC}

and

\frac{AB}{BC} = \frac{50}{x}

\Rightarrow \tan 30^{\circ} = \frac{50}{x}

\Rightarrow \frac{1}{\sqrt{3}} = \frac{50}{x}

\Rightarrow x = 50 \sqrt{3} m

So, the length of the shadow is

50 \sqrt{3} m .

Hence, the correct option is 2.

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