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From the top of a tower 50 m high the angles of depression of the top and bottom of a pole are observed to be $45 °$ and $60 °$ respectively. Find the height of the pole.

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50 (3 − 1) 3 m

100 (3 − 1) 3 m

150 (3 − 1) 3 m

200 (3 − 1) 3 m

answer is A.

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Detailed Solution

Given that the height of the tower is 50 m,
We have to find the height of the pole.
From the top of a 50 m high tower, the angles of depression of the top and bottom of a pole are observed to be 45^o and 60^o respectively. Find the height

From the top of a 50 m high tower, the angles of depression of the top and bottom of a pole are observed to be 45^o and 60^o respectively. Find the height

In a right-angle triangle

tan θ = Opposite side Hypotenuse

Let the height of the pole be h and the distance between the pole and tower be x. It can be observed that,

tan 60 ° = 50 x ⇒ 3 = 50 x ⇒ x = 503

And,

tan 45 ° = 50-h x ⇒ 1 = 50-h x ⇒ 50-h = x ⇒ 50-h = 503 ⇒ h = 50- 503 ⇒ h = 50(3 -1) 3

The height of the pole is

50 (3 − 1) 3 m

.
Therefore, the correct option is 1.

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