Question

The angle of elevation of the top of pillar from the foot of the statue is ${30}^{\circ }$ and the angle of elevation of the top of the statue from the foot of the pillar is ${60}^{\circ }$. If the statue is 100 m high, find the height of the pillar.

• A. 50 m
• B.
• C.
• D. None of these

Answer 1

The correct option is C

In this figure; AB = 100 m, $\angle$DBC = ${30}^{\circ }$ and $\angle$ ACB = ${60}^{\circ }$; we have to find CD.

In $\Delta$ ABC;

tan ${60}^{\circ }$ = AB/BC

$\Rightarrow$ BC = 100/3

In $\Delta$ DBC;

tan ${30}^{\circ }$ = CD/BC

$\Rightarrow$ CD = 100/3 = $33\frac{1}{3}$ m