If a pole 6 m high casts a shadow 2\sqrt3m long on the ground, then Sun’s elevation is:

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Solution

Q.
If a pole 6 m high casts a shadow $2 \sqrt{3} m$ long on the ground, then Sun’s elevation is:

1 $60 °$

2 $45 °$

3 $30 °$

4 $90 °$

Ans.
(1)

Let AB be the pole of height 6 m. Let θ be the angle of elevation of Sun and BC be the shadow of the pole. Then,

$∠ A C B = θ, A B = 6 m a n d B C = 2 \sqrt 3 m I n △ A B C, r i g h t a n g l e d a t B,$

$\tan C = A B / B C \Rightarrow \tan θ = 6 / 2 \sqrt 3 = \sqrt 3$

$\Rightarrow t a n θ = t a n 60^{\circ} \Rightarrow θ = 60^{\circ}$

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