Question

An observer, $2m$ tall is $10\sqrt{3}m$ away from a tower. The angle of elevation from his eye to the top of the tower is ${30}^{\circ }$. What is the height of the tower?

• A. $12m$
• B. $14m$
• C. $10m$
• D. $15m$

Answer 1

The correct option is A $12m$


$SR=PQ=2m$
$PS=QR=10\sqrt{3}m$
$\tan {30}^{\circ }=\frac{TS}{PS}$
$\frac{1}{\sqrt{3}}=\frac{TS}{10\sqrt{3}}$
$TS=\frac{10\sqrt{3}}{\surd 3}=10m$
$TR=TS+SR=10+2=12m$