Question

Two poles of different heights are erected from the ground. If the smaller pole is 20 m high and distance between 2 poles are 10 m, and the angle of elevation of the tip of the longer pole from that of the shorter pole is ${60}^{\circ }$, find the length of the second pole.

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

Answer 1

The correct option is D

$20+10\sqrt{3}m$

Distance between the 2 poles, AC =10m
Height of the shorter pole, AE =CD =20m

BC = $x$
Consider the right angled triangle ABC,
$tan{60}^{\circ }=\frac{oppositeside}{adjacentside}=\frac{BC}{AC}=\frac{x}{10}$
$x=10\times tan{60}^{\circ }$
$tan{60}^{\circ }=\sqrt{3}$
$x=10\sqrt{3}m$
Height of second pole = $CD+BC=20+10\sqrt{3}m$