Question

The angle of elevation of the top of a tower from a point $A$ in east of it is ${45}^{\circ }$. The angle of elevation of the top of the same tower from point $B$ which is in south of $A$ is ${30}^{\circ }$. If the distance between $A$ and $B$ is $30\sqrt{2}\text{m}$, then height (in metre) of the tower is

Answer 1

Let the height of tower be $x$ and its base be $O$.

$\therefore OA=x$


$\therefore OB=\sqrt{3}x$

Now,

$\therefore (30\sqrt{2}{)}^2+x^2=(\sqrt{3}x{)}^2$
$\Rightarrow x=30$
$\therefore$ Height of the tower is $30\text{m}$.