Question

Three poles $A,B$ and $C$ are in a straight line, apart by $10$ metres each. The height of pole $A$ is $20$ metres and the angle of depression from the top of pole $A$ to the top of pole $B$ is ${60}^{\circ }$ and the angle of elevation from the top of pole $B$ to the top of pole $C$ is ${30}^{\circ }.$ The height (in metres) of pole $C$ is

• A. $\frac{10}{3}(3-\sqrt{3})$
• B. $\frac{20}{3}(3+\sqrt{3})$
• C. $\frac{20}{3}(3-\sqrt{3})$
• D. $\frac{10}{3}(3+\sqrt{3})$

Answer 1

The correct option is C $\frac{20}{3}(3-\sqrt{3})$


Let height of pole $B$ be $h$ and height of pole $C$ be $H.$
Then, $\tan {60}^{\circ }=\frac{20-h}{10}$
$\Rightarrow h=20-10\sqrt{3}$

Again, $\tan {30}^{\circ }=\frac{H-h}{10}$
$\Rightarrow \frac{10}{\sqrt{3}}=H-h\Rightarrow H=h+\frac{10}{\sqrt{3}}\Rightarrow H=20-10\sqrt{3}+\frac{10}{\sqrt{3}}\Rightarrow H=\frac{20(\sqrt{3}-1)}{\sqrt{3}}=\frac{20}{3}(3-\sqrt{3})$