Question

From a point on the ground, the angles of elevation of the bottom and top of a water tank kept on the top of the $30$ m high building are ${30}^{\circ }$ and ${45}^{\circ }$ respectively. Find the height of the water tank.

Answer 1

$tan{45}^0=\left(\frac{h+30}{b}\right)orb=h+30nowtan{30}^0=\left(\frac{30}{b}\right)or\left(\frac{1}{\sqrt{3}}\right)=\left(\frac{30}{h+30}\right)orh+30=30\sqrt{3}orh=30\sqrt{3}-30=30(\sqrt{3}-1)=21.96m$