Question

Two lamps posts are $60$ metres apart, and the height of the one is double that of the other. From the middle of the line joining their feet, an observer finds the angular elevation of their top to be complimentary. Find the height of each lamp.

• A. $52.63m$; $85.22m$
• B. $46.53m$; $71.39m$
• C. $20.63m$; $22.32m$
• D. $21.21m$; $42.42m$

Answer 1

The correct option is D $21.21m$; $42.42m$

Consider the given figure
$\tan \theta =\frac{2h}{30}$
And
$\tan ({90}^0-\theta )=\cot \theta =\frac{h}{30}$
Hence
$\frac{h}{30}=\frac{30}{2h}$
or
$2h^2=900$
$h=\frac{30}{\sqrt{2}}m$
$=15\sqrt{2}m$
Hence the heights are $15\sqrt{2}m,30\sqrt{2}m$.