Question

Two pillars of equal height stand at a distance of $100$ metres. $A$t a point between them the elevation of their tops are found to be ${30}^o$ and ${60}^0$ Then height of the each pillar in metres is

• A. $25\sqrt{3}$
• B. $20\sqrt{3}$
• C. $50\sqrt{3}$
• D. $35\sqrt{3}$

Answer 1

Answer: (A)

$25\sqrt{3}$

Let's ${}^{\prime }{h}^{\prime }$ be the height of each pillar and $d$ is distance from one pillar to the point.

$\tan {30}^0=\frac{h}{d}$

$d=h\sqrt{3}$

$\tan {60}^o=\frac{h}{100-d}$

$100-h\sqrt{3}=\frac{h}{\sqrt{3}}$

Simplify further,

$100\sqrt{3}-3h=h$

Thus,

$h=25\sqrt{3}m.$