Question

From the top of a tower $100m$ high, the angels of depression of the bottom and the top of a building just opposite to it are observed to be ${60}^{\circ }$ and ${45}^{\circ }$ respectively, then height of the building is:

• A. $\frac{100\left(3-\sqrt{3}\right)}{3}m$
• B. $\frac{100\left(3+\sqrt{3}\right)}{3}m$
• C. $\frac{3+\sqrt{3}}{3}m$
• D. $\frac{50\left(3-\sqrt{3}\right)}{3}m$

Answer 1

The correct option is A $\frac{100\left(3-\sqrt{3}\right)}{3}m$

$AC=100-h$

$\tan {45}^{\circ }=\frac{100-h}{x}=1$

$\Rightarrow 100-h=x$

Now, $\tan {60}^{\circ }=\frac{100}{x}=\sqrt{3}$

$\frac{100\sqrt{3}}{3}=x$

Now $h=100-\frac{100\sqrt{3}}{3}=100(1-\frac{\sqrt{3}}{3})=\frac{100}{3}(3-\sqrt{3})$