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The angle of elevation at the top of a tower from a point 10 m from the foot of the tower is $30 ° .$ The height of the tower is

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10 \sqrt{3}

\frac{10}{\sqrt{3}}

\frac{10}{3}

10 m

answer is B.

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Detailed Solution

It is given that the angle of elevation at the top of a tower from a point 10 m from the foot of the tower is

30^{\circ} .

According to the given data, the figure has been drawn below.
Question Image

ΔABC,

tan θ = P e r p e n d i c u l a r b a s e

\tan 30 ° = \frac{AB}{BC}

\Rightarrow \frac{1}{\sqrt{3}} = \frac{h}{10}

∵ tan 30 ° = 13

\Rightarrow h = \frac{10}{\sqrt{3}}

So the height of the tower is

\frac{10}{\sqrt{3}}

.
So, the correct option is 2.

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