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The length of shadow of a tower on the plane ground is $\sqrt{3}$ times the height of the tower. The angle of elevation of sun is

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45 °

°

°

90 °

answer is B.

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Detailed Solution

It is given that the length of shadow of a tower on the plane ground is

\sqrt{3}

times of the height of the tower.
According to the given data the figure has been drawn below.
Question Image

Let, the height of the tower be h meter. Then the length of the tower be

\sqrt{3} h

meter

∴

△ ABC

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

\Rightarrow tanθ = \frac{AB}{BC}

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

\Rightarrow tanθ = \frac{1}{\sqrt{3}}

\Rightarrow tanθ = \tan 30 °

(

∵ \tan 30 ° = \frac{1}{\sqrt{3}}

)

\Rightarrow θ = 30 °

So, the angle of elevation of sun is

30 °

.
So, the correct option is 2.

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