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+1 vote
1.5k views
in Trigonometry by (34.5k points)
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The length of shadow of a tree of 8 m long, When the sun’s angle of elevation is 45° is ……………… m.

A) 8/√3

B) 8 √3

C) 8

D) 16 √3

2 Answers

+1 vote
by (66.4k points)
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Best answer

Correct option is: C) 8

Sun's angle of elevation is \(45^\circ\) 

\(\therefore\)  \(\angle\)CAB = \(45^\circ\)

The height of tree be BC = 8m.

In right  \(\triangle\)ABC,

tan A = \(\frac {BC}{AB}\) \(\Rightarrow\) AB = \(\frac {BC}{tan \, 45^\circ}\) (\(\because\) \(\angle\)A = \(45^\circ\))

\(\Rightarrow\) AB = BC (\(\because\) tan \(45^\circ\) = 1)

\(\Rightarrow\) AB = 8m (\(\because\) BC = 8m)

Hence, the length of the shadow of tree is 8m.

+2 votes
by (35.6k points)

Correct option is: C) 8

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