Question

From the top of a building h metres high, the angle of elevation of a monument is ${45}^o$ and angle of depression of its foot is ${30}^o$. The height of the monument is

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

Answer 1

Answer: (D)

$(\sqrt{3}+1)h$

In $\Delta ADB$

$AB=\frac{h}{tan{30}^{\circ }}$

In $\Delta DCF,FC=CDtan{45}^{\circ }$

But $AB=CD$

$\to \frac{h}{tan{30}^{\circ }}=\sqrt{3}h$

Thus, $FC=\sqrt{3}h$

Total height of monument $=BC+FC$

$=h+\sqrt{3}h$

$=(\sqrt{3}+1)h$