Question

The angles of elevation of the top of a tower from the points P and Q at distance of 'a' and 'b' respectively from the base of the tower and in the same straight line with it are complementary. The height of the tower is:

• A. $\sqrt{ab}$
• B. $\frac{a}{b}$
• C. ab
• D. $a^2{b}^2$

Answer 1

The correct option is A $\sqrt{ab}$

In $\Delta AOB$, $\tan \theta =\frac{OA}{a}$

In $\Delta AOC$, $\tan (30-\theta )=\cot \theta =\frac{OA}{b}$

$\Rightarrow \tan \theta =\frac{b}{OA}$

$\Rightarrow \frac{OA}{a}=\frac{b}{OA}$

$\Rightarrow O{A}^2=ab$

$\Rightarrow OA=\sqrt{ab}$

$\Rightarrow \left(A\right)$.