Question

The angle of elevation of the top of a pole from the point $A$ on ground is ${45}^{\circ },$ whereas the angle of depression of the foot of pole from the point which is $10$ feet above point $A$ is ${30}^{\circ }.$ Then the length of the pole is

• A. $5\sqrt{3}$ feet
• B. $20\sqrt{3}$ feet
• C. $\frac{10}{\sqrt{3}}$ feet
• D. $10\sqrt{3}$ feet

Answer 1

The correct option is D $10\sqrt{3}$ feet

Let length of pole be $h.$

In $△ABD$
$\tan {30}^{\circ }=\frac{10}{x}$
$\Rightarrow x=10\sqrt{3}\dots \left(1\right)$

and in $△ABC$
$\tan {45}^{\circ }=\frac{h}{x}$
$\Rightarrow x=h\dots \left(2\right)$
From $\left(1\right)$ and $\left(2\right),$
$h=10\sqrt{3}$ feet