Question

A man looks from the top of a vertical tower 30 metres high at a marked point upon the horizontal plane on which the tower stands. The angle of depression of this point is ${30}^0.$ The distance of the marked point from the foot of the tower is

• A. $\frac{30}{\sqrt{3}}$m
• B. $\frac{30\sqrt{3}}{2}$m
• C. 30 m
• D. $30\sqrt{3}$m

Answer 1

Answer: (D)

$30\sqrt{3}$m

Consider the above diagram
In triangle POM
Let $OM$ be the height of the tower
Let $OP$ be the horizontal distance of the marked point from the foot of the tower
It is given that angle of depression$=P={30}^0$
Therefore
$\frac{MO}{PO}$
$=\frac{30m}{PO}$
$=tan{30}^0=\frac{1}{\sqrt{3}}$
Therefore $PO=30\sqrt{3}$ metres
Hence answer is D