Question

The angle of elevation of the top of an incomplete vertical pillar at a horizontal distance of 100 m from its base is ${45}^{\circ }$. If the angle of elevation of the top of the complete pillar at the same point is to be ${60}^{\circ }$, then the height of the incomplete pillar is to be increased by :

• A. $50\sqrt{2}$
• B. $100$
• C. $100(\sqrt{3}-1)$
• D. $100(\sqrt{3}+1)$

Answer 1

Answer: (C)

$100(\sqrt{3}-1)$

Let $D$ be the fixed point, $AC$ be the pillar

$\Rightarrow CD=100$m

$AB$ is the height to be increased.

In $△BCD,\tan {45}^{\circ }=\frac{BC}{DC}$

$\Rightarrow 1=\frac{BC}{DC}=\frac{BC}{100}$

In $△ACD,\tan {60}^{\circ }=\frac{AC}{DC}$

$\Rightarrow \sqrt{3}=\frac{AC}{100}$

$\Rightarrow AC=100\sqrt{3}$m

Height to be increased$=AB=AC-BC=100\sqrt{3}-100=100(\sqrt{3}-1)$m

$\therefore$ to complete the pillar $100(\sqrt{3}-1)$m has to be increased.