Question

A man walking due North, observes that the elevation of a balloon, which is due East of him and is sailing towards the North-West is then ${60}^{\circ }$; after he has walked $400yards$ the balloon is vertically over his head. Find its height, supposing it is have always remained the same.

Answer 1

$AQ=hcot{60}^o$ $\therefore AQ=\frac{h}{\sqrt{3}}$
As the man walks AB = 400 towards North the balloon sailing towards the North-West comes to position R above B, as it is seen vertically over his head. From the figure
$\angle AQB=\angle ABQ={45}^o$
$\therefore AB=AQ=\frac{h}{\sqrt{\left(3\right)}}$
or $400=\frac{h}{\sqrt{\left(3\right)}}$ $\therefore h=400\sqrt{3}$