Question

Fill in the blanks
A tower is observed from two stations A and B where B is East of A at a distance 100 metres. The tower is due North of A and due North-West of B. The angles of elevation of the tower from A and B are complementary, the height of the tower is ____________.

Answer 1

$100(2{)}^{1/4}$
$h=APtan\theta =BPcot\theta$
$\therefore h^2=AP.BP$, $BP=100\sqrt{2}$ by Pythagoras.
$\therefore h^2=100\times 100\sqrt{2}$ or $h=100(2{)}^{1/4}$