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. 34 m
• C. 50√3 m
• D. 100/3 m
• E. None of these

Answer 1

The correct option is D

100/3 m

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