Question

The angles of elevation of the top of a tower from two points at distances $m$ and $n$ meters 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)

$\sqrt{mn}$

$In△ABD,\tan \theta =\frac{AB}{BD}=\frac{h}{m}...\left(1\right)In△ABC,\tan (90-\theta )=\frac{AB}{BC}=\frac{h}{n}\cot \theta =\frac{h}{n}\tan \theta =\frac{n}{h}Usingequation\left(1\right),\frac{h}{m}=\frac{n}{h}{h}^2=mnh=\sqrt{mn}$