Question

Two vertical lamp-posts of equal height stand on either side of a road 50m wide.At a point P on the road between them.Elevation of the tops of the lamps are 60 &30.Find the distance of P from the lamp post which makes angle of 60?

• A. $25m$
• B. $12.5m$
• C. $16.5m$
• D. $20.5m$

Answer 1

Answer: (B)

$12.5m$

Let AB and CD be the lamp posts of height h.
Now As BC=50,Let $BP=x$
therefore $PC=50-x$ .we have to find x.
In triangle$BPA,\frac{h}{x}=\tan 30=\sqrt{3}$
$h=x\sqrt{3}$ ...(1)
In triangle$PCD,\frac{h}{50-x}=\tan 30=\frac{1}{\sqrt{3}}$
$h=\frac{50-x}{\sqrt{3}}$..(2)
from (1) and (2)
$x\sqrt{3}$ =$\frac{50-x}{\sqrt{3}}$
$3x=50-x$
$4x=50$
$x=\frac{50}{4}=12.5m$