Question

From the top of tower $100m$ height, a man observes two cars on the opposite side of tower with angles of depression ${30}^{\circ }$ and ${45}^{\circ }$respectively. Find the distance between cars.

Answer 1

REF.Image.

In $\Delta BCD$

$\tan {45}^{\circ }=\frac{100}{BD}$

$BD=100$

In $\Delta ACD$

$\tan {30}^{\circ }=\frac{100}{AD}=\frac{1}{\sqrt{3}}$

$AD=100\sqrt{3}$

$AB=100+100\sqrt{3}=100(\sqrt{3}+1)=273.2m$

Hence, this is the answer.