Question

The angles of elevation of the top of a tower from two points at distance m and n metres are complementary. If the two points and the base of the tower are on the same straight line, then the height of the tower is

• A. $\sqrt{mn}$
• B. mn
• C. $\frac{m}{n}$
• D. None of these

Answer 1

Answer: (A)

$\sqrt{mn}$

From $\Delta ADB,$
$\frac{h}{m}=tan\theta$

From $\Delta ABC,$
$\frac{h}{n}=tan(90-\theta )$

$=cot\theta$

$\therefore \frac{h}{m}\times \frac{h}{n}=tan\theta \times cot\theta$

$=1$

$\Rightarrow h=\sqrt{mn}$