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If a pole stands vertically on the ground if the angle of elevation at the top of the pole from a point 60 m away from the pole is $30^{o}$ , then what is the height of the pole?

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34.2 m

34.3 m

34.4 m

34.6 m

answer is D.

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Detailed Solution

It is given that a pole stands vertically on the ground if the angle of elevation at the top of the pole from a point 60 m away from the pole is

30^{o}

.
Let AB represents the pole, O is angle of elevation at the top of the pole from a point

60 m

away from the pole.
Question Image

Then, OA = 60 m,

∠

O =

30^{o}

.
In △ BOA, ∠ A is right angle,

\tan 30^{o} = \frac{AB}{OA}

⇒

\frac{1}{\sqrt{3}} = \frac{AB}{60}

⇒

AB = \frac{60}{\sqrt{3}} = 20 \sqrt{3}

⇒

AB = 20 \times 1.73

…

(\sqrt{3} = 1.73)

.
⇒

AB = 34.6 m

Height of the pole is 34.6 m
Hence, the correct option is 4.

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