Question

From the base of a tower the angle of elevation of the top of the cliff is 60${}^o$ and from the base of the cliff, the angle of elevation of the top a tower is 30${}^o$. If the height of the tower is 50 m, then the height of the cliff is :

• A. $50\sqrt{3}$ m
• B. $150$ m
• C. $100$m
• D. $50$ m

Answer 1

The correct option is B $150$ m

Let AB be the cliff and CD be the tower.

Then, $\angle$ BDA = 60${}^o$ and $\angle$CBD = 30${}^o$.

Also, $CD=50$ m.

In $△$CDB,
tan 30${}^o$ = $\frac{CD}{BD}\Rightarrow \frac{1}{\sqrt{3}}=\frac{50}{BD}\Rightarrow$ 50$\sqrt{3}$

In $△$ABD,
tan 60${}^o$ = $\frac{AB}{BD}\Rightarrow \sqrt{3}=\frac{AB}{50\sqrt{3}}\Rightarrow$ AB = 150

$\therefore$ Height of the cliff is 150 m.