Question

The angle of elevations of the top of the tower from the points distance $a$ and $b$ from the base of tower $(a>b)$ are ${30}^o$ and ${60}^o$, then height of tower is _____________.

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

Answer 1

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

In the given figure let h be the height of the tower.

Now, from the given figure -

$tan{60}^o=$$\frac{h}{b}$$=\sqrt{3}$ .....$1$

$tan{30}^o=$$\frac{h}{b}$$=\frac{1}{\sqrt{3}}$ .....$2$

Multiplying,$1$ and $2$

We get,

$1=$$\frac{h^2}{ab}$

Hence,$h^2=ab$

Therefore,$h=\sqrt{ab}$

Hence,Option (c) is correct.