Question

If the angles of elevation 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 ______.

Options

• `sqrt(a/b)`

• `sqrt(ab)`

• `sqrt(a + b)`

• `sqrt(a - b)`

Answer 1

If the angles of elevation 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 `underlinebb(sqrt(ab))`.

Explanation:

`h/a = tan θ`

⇒ h = a tan θ   ...(i)

`h/b = tan(90^circ - θ) = cot θ`

⇒ h = b cot θ   ...(ii)

From (i) and (ii), we get

h² = ab and hence `h = sqrt(ab)`.