Question

If the angles of elevation of the top of the tower from two points at distances of a
and b cm from the base of the tower and in the same straight line with it, are comple-
mentary, then show that the height of the tower is √ab.​

Answer 1

Hello Mate,

Here is your answer,

Let us say that 'C' and 'D' are the two points at distances 'a' and 'b' from the base of the tower,

Given:

• The angles of elevation are complementary

So,

• Angle ADB = $\alpha$

• Angle ACB = $90 - \alpha$

Solution:

In triangle ACB,

• $\tan( \alpha ) = \frac{ab}{bd} \\ \\ \tan( \alpha ) = \frac{h}{a} \: \: \: \: \: \: \: ....(1)$

In triangle ADB,

• $\tan(90 - \alpha ) = \frac{ab}{bc} \\ \\ \cot( \alpha ) = \frac{h}{b} \: \: \: \: \: \: ....(2)$

Multiply eq(1) with eq(2) we get,

$\tan( \alpha ) \times \cot( \alpha ) = \frac{h}{a} \times \frac{h}{b} \\ \\ \frac{ {h}^{2} }{ab} = 1 \\ \\ {h}^{2} = ab \\ \\ h = \sqrt{ab}$

Hope it helps:)

Answer 2

Answer:

Check your answer please