Geometry

Trigonometry

Medium

If the angles of elevations of the top of a tower from two points at distances a and b from the base and in the same straight line with it are complementary then the height of the tower is

$\sqrt{\dfrac{a}{b}}$

$\sqrt{ab}$

$\sqrt{a+b}$

$\sqrt{a-b}$

✅ Correct Option: 2

Let the height be $h$ and the angles be $\theta$ and $90-\theta$ .

From the first point, $\tan\theta = h/a$ . From the second, $\tan(90-\theta) = \cot\theta = h/b$ .

Multiplying, $\tan\theta \cdot \cot\theta = 1 = h^2/(ab)$ , so $h^2 = ab$ and $h = \sqrt{ab}$ .

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Solution

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