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At a point P on the ground, the angles of elevation of the top of a 10 m tall building, and of a helicopter covering some distance over the top of the building, are $30 °$ and $60 °$ respectively. What will be the height of the helicopter above the ground?

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10m

20m

30m

35m

answer is B.

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Detailed Solution

Given that,
The angle of elevation of the top of the building at P =

30 °

The angle of elevation of a helicopter covering distance over the top of the building =

60 °

The height of the building =

10 m

.
Considering the distance from the point P to C=y and A to B = x and BC as the height of the building.
We draw the diagram,
Question Image

Using

tan θ = h e i g h t b a s e

.
Then in triangle BPC,

tan 30 ° = B C P C ⇒ 13 = 10 y [∵ tan 30 ° = 13] ⇒ y = 103 m

Using the trigonometric ratio formula in the

Δ A C D

tan 60 ° = A C P C ⇒ 3 = x + 10 y [∵ tan 60 ° = 3] ⇒ x = 3 y − 10

Substituting

y = 103

in the equation

x = 3 y − 10

⇒ x = 3 y − 10 ⇒ x = 3103 − 10 ⇒ x = 30 − 10 ⇒ x = 20 m

Thus the height of the helicopter from the ground will be 20 m.
Therefore the correct option is 2.

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