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The angle of elevation $θ$ of a vertical tower from a point on the ground is such that its tangent is $\frac{5}{12}$ . On walking $192$ metres towards the tower in the same straight line the tangent of angle of elevation $ϕ$ is found to be $\frac{3}{4}$ . Find the height of the tower.

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170

175

180

185

answer is C.

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Detailed Solution

It is given that the angle of elevation

θ

of a vertical tower from a point on the ground is such that its tangent is

\frac{5}{12}

.
On walking

192

metres towards the tower in the same straight line the tangent of angle of elevation

ϕ

is found to be

\frac{3}{4}

.
Let PQ be the tower and R be the point of observation.
Question Image

ΔPQR,

tanθ = \frac{h}{192 + x} = \frac{5}{12}

⇒

x = \frac{1}{5} (12 h - 960)

...(1)
In

ΔPQS,

tanϕ = \frac{h}{x} = \frac{3}{4}

⇒

x = \frac{4 h}{3}

...(2)
From (1) and (2), we get,
⇒

\frac{4 h}{3} = \frac{1}{5} (12 h - 960)

⇒

h = 180

∴

The height of the tower is 180 m.
Hence, the correct option is 3.

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