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The angles of elevation of the top of a tower from two points at a distance, $x$ and $y$ metres from the base and in the same straight line with it are complementary. Find the height of the tower.

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h = \sqrt{xy}

h = \frac{x}{y}

h = \sqrt{y}

h = \sqrt{x}

answer is A.

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Detailed Solution

It is given that the angles of elevation of the top of a tower from two points at a distance,

x

and

y

metres from the base and in the same straight line with it are complementary.
Let the height of the tower be

h .

In right angled

△ ABC

tanθ = \frac{h}{x}

…. (1)
In right

△ ABD

\tan (90 - θ) = \frac{h}{y}

… (2)
From

(1)

and

(2)

, we get,
⇒

tanθ \times \tan (90 - θ) = \frac{h}{x} \times \frac{h}{y}

⇒

tanθ \times cotθ = \frac{h^{2}}{xy}

⇒

h^{2} = xy

⇒

h = \sqrt{xy}

Hence, the correct option is 1.

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