Question

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

The correct option is B

$100$

AB is the height of incomplete tower. $\angle B={90}^{\circ }$
$tan{45}^{\circ }=\frac{AB}{BC}$
AB = 100 m
Let height of AD be x
BD = AB + DA = (100+x)

For $\Delta DBC,tan{60}^{\circ }=\frac{DB}{BC}$
$\sqrt{3}=\frac{(100+x)}{100}$
$\frac{100+x}{100}=\sqrt{3}$
$x=100(\sqrt{3}-1)m$