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An observer, 1.7 m tall, is $203$ m away from a tower. The angle of elevation from the eye of observer to the top of tower is $30 °$ . Find the height of tower.

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25.0 m

20.0 m

30.0 m

21.7 m

answer is B.

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Detailed Solution

Given that an observer, 1.7 m tall, is

203

m away from a tower. The angle of elevation from the eye of observer to the top of tower is

30 °

. We have to find the height of the tower.
In a right-angle triangle

tan θ = Opposite side Hypotenuse

Consider has the height of the tower.
Question Image

So,

A B = h

and

A E = h − 1.7

.
And,

B C = D E = 203

In △ A D E, ∠ E = 90 °

Therefore,

cos 30 ° = h − 1.7 203 ⇒ 13 = h − 1.7 203 ⇒ h − 1.7 = 20 ⇒ h = 20 + 1.7 Therefore, h = 21.7 m

The height of the tower is h = 21.7m.
Therefore, the correct option is 2.

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