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From a point P on the ground, the angle of elevation of the to

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From a point P on the ground, the angle of elevation of the top of a $10 m$ tall building and a helicopter, hovering over the top of the building, are $3 0^{\circ}$ and $6 0^{\circ}$ respectively. Find the height of the helicopter above the ground.

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From a point P on the ground, the angle of elevation of the top of a

10 m

tall building and a helicopter, hovering over the top of the building, are

3 0^{\circ}

and

6 0^{\circ}

respectively. Find the height of the helicopter above the ground.

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Text solutionVerified

Given

A C = 10, ∠ A BC = 30, ∠ A B D = 60, l e t C D = h

From

△ A BC

A B = \frac{A C}{tan 30} = 103 .............. (1)

From

△ A B D

A B = \frac{A D}{tan 60} = \frac{10 + h}{tan 60} ............. (2)

From 1 and 2

we get

103 = \frac{10 + h}{3}

h = 20 m

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Question Text	From a point P on the ground, the angle of elevation of the top of a $10 m$ tall building and a helicopter, hovering over the top of the building, are $3 0^{\circ}$ and $6 0^{\circ}$ respectively. Find the height of the helicopter above the ground.
Answer Type	Text solution:1
Upvotes	150