Question

From the top of the cliff $150m$ high the angles of depression of the top and bottom of a tower are observed to be ${30}^{\circ }$ and ${60}^{\circ }$ respectively. The height of the tower is

• A. $100m$
• B. $50\sqrt{3}m$
• C. $133\frac{1}{3}$
• D. $100(\sqrt{3}-1)$

Answer 1

Answer: (A)

$100m$

$BF=(150-x)m.$ Let $AC=y$
$\tan {30}^0=\frac{150-x}{y}$
$\tan {60}^0=\frac{150}{y}$
$\Rightarrow y=(150-x)\sqrt{3}=\frac{150}{\sqrt{3}}$
$\therefore 150-x=50$ or $x=100m$