Question

The angles of elevation of the top of a tower from two points at distances ‘a’ and ‘b’ metres from the base and in the same straight line with it, are complementary. The height of the tower is:

• A. ab metres
• B. $\sqrt{ab}$ metres
• C. $\frac{a}{b}$ metres
• D. (a + b) metres

Answer 1

The correct option is B

$\sqrt{ab}$ metres

$\tan ({90}^0-\theta )=\frac{AB}{a}$

AB = $a.\cot \theta$

Again, $\tan \theta$ = $\frac{AB}{b}$

AB = $b.\tan \theta$

$A{B}^2$ = ab

AB = $\sqrt{ab}$