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The angle of elevation of the top of a vertical tower from a point on the ground is $60 °$ . From another point $10 m$ vertically above the first, its angle of elevation is $30 °$ . Find the height of the tower.

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5 m

10 m

15 m

20 m

answer is C.

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Detailed Solution

Given that the angle of elevation of the top of a vertical tower from a point on the ground is

60 °

. From another point 10 m vertically above the first, its angle of elevation is

30 °

.
We have to find the height of the tower.

In a right-angle triangle, tan θ = Opposite side Hypotenuse

Let the height of the tower be

h cm .

Now, In

Δ PAB

tan 60 ° = A P A B ⇒ 3 = h A B ⇒ A B = h 3 − − − − (1)

And, In

Δ PCD

tan 30 ° = PD CD ⇒ 13 = h-10 CD ⇒ CD= 3 (h-10)----(2)

Since,

AB = CD,

So, equation (2) becomes,

AB = 3 (h-10)----(3)

Equating equation (1) and (3), we get,

⇒ h 3 = 3 (h-10) ⇒ h = 3(h-10) ⇒ 2 h = 30 ⇒ h = 15 m

Hence, the height of the tower will be 15 m.
Therefore, the correct option is 3.

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