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The length of the shadow is of 5 m height tree whose angle of elevation of the sun is 30° is

A) 5 m 

B) √3 m 

C) 5 √3 m 

D) 10 m

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2 Answers

+1 vote
by (34.0k points)

Correct option is: C) 5 √3 m

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edited ago by

Correct option is: C) 5 √3 m

Given that angle of elevation of the sun is \(30^\circ\).

i.e, \(\angle\)CAB = \(\angle\)A = \(30^\circ\)

Height of the tree is BC = 5 cm.

In right \(\triangle\) ABC,

tan A = \(\frac {BC}{AB}\)

\(\frac {BC}{AB}\) = tan \(30^\circ\) = \(\frac {1}{\sqrt3}\) (\(\because\) \(\angle A=30^\circ\))

\(\Rightarrow AB=BC\sqrt 3=5\sqrt3m(\because BC=5m)\)

Hence, the length of the shadow of the tree is \(5 \sqrt3\) m.

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