From a point on the level ground, the angle of elevation of the top of a pole is $30^{\circ}$ on moving 20 metres nearer, the angle of elevation is $45^{\circ}$. Then, the height of the pole (in metres), is

• A

  $10(\sqrt{3}-1)$
• Correct answer
  B

  $10(\sqrt{3}+1)$
• C

  $15$
• D

  $20$

Solution

In $\triangle B D A$,

$\tan 45^{\circ}=\frac{h}{x} \Rightarrow h=x$
In $\triangle B A C$,
$\begin{aligned}<br />\tan 30^{\circ} & =\frac{h}{20+x} \\<br />\frac{1}{\sqrt{3}} & =\frac{x}{20+x} \\<br />20+x & =\sqrt{3} x \\<br />x=\frac{20}{\sqrt{3}-1} & =\frac{20}{2}(\sqrt{3}+1) \\<br />& =10(\sqrt{3}+1) \mathrm{m}<br />\end{aligned}$
[from Eq. (i)]

Hence, the correct answer is option: 'B'.