Question

The angle of elevation of a tower from a point is ${30}^{\circ }$. At a point on the horizontal line passing through the foot of the tower and $50$ metres nearer it, the angle of elevation is ${60}^{\circ }$. The distance of the first point from the tower is

• A. $50\text{m}$
• B. $75\text{m}$
• C. $100\text{m}$
• D. $150\text{m}$

Answer 1

The correct option is D $150\text{m}$

From $△ADB\Rightarrow \frac{AB}{DB}=\tan {60}^0$

$\Rightarrow AB=50\sqrt{3}$

also, $\frac{AB}{50+x}=\tan {30}^0\Rightarrow \frac{50+x}{\sqrt{3}}=50\sqrt{3}$

$\Rightarrow 50+x=150$

$\Rightarrow x=100\text{m}$

Therefore $CB=150\text{m}$