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The length of shadow of a tree is $16 m$ when the angle of elevation of the sun is $60 °$ . What is the height of the tree?

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8

16

16 \sqrt{3}

\frac{16}{\sqrt{3}}

answer is C.

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Detailed Solution

It is given that the length of shadow of a tree =

16 m

, angle of elevation of the sun=

60^{\circ}

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

Let

AB = h

be height of the tree and

BC

be it's shadow.
In

△ ABC

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

\tan 60 ° = \frac{AB}{BC}

\Rightarrow \frac{h}{16} = \tan 60 °

\Rightarrow h = \tan 60 ° \times 16

\Rightarrow h = 16 \sqrt{3}

(\tan 60 ° = \sqrt{3})

∴

Height of the tree is

16 \sqrt{3} m .

So the correct option is 3.

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