Question

From the top of a building $21\text{m}$ high, the angle of elevation and depression of the top and the foot of another buillding are ${30}^{\circ }$ and ${45}^{\circ }$ respectively. The height of the second building is

• A. $21+7\sqrt{3}$
• B. $21\sqrt{3}$
• C. $21\sqrt{3}+7$
• D. $7\sqrt{3}$

Answer 1

The correct option is A $21+7\sqrt{3}$

Let $AD=21\text{m}$ is the height of first building and $BE$ is second building
Consider $CE=x\text{m}$

From $△ABD,$
$\tan {45}^{\circ }=\frac{21}{AB}\Rightarrow AB=21\text{m}$

Now, from $△DCE,$
$\tan {30}^{\circ }=\frac{x}{DC}\Rightarrow x=\frac{21}{\sqrt{3}}=7\sqrt{3}\text{m}$

Hence, height $BE=21+7\sqrt{3}\text{m}$