Question

The horizontal distance between the building and the lamp-post

• A. $86.67m$
• B. $60m$
• C. $57m$
• D. $34.64m$

Answer 1

The correct option is D $34.64m$

Let the height of the lamp post be h.
Let the distance between the foot of the lamp post and the foot of the tower be y.
Hence
$\tan {30}^0=\frac{1}{\sqrt{3}}=\frac{60-h}{y}$
Hence
$y=\sqrt{3}(60-h)$ ...(i)
And
$\tan {60}^0=\sqrt{3}=\frac{60}{y}$ ...(ii)
Hence
$y=20\sqrt{3}=34.64m$