Question

The angle of elevation of the top of a flag post (AB) from a point (C) on a horizontal ground is found to be ${30}^o$. On walking 6 m towards the post at X, the angle of elevation is found to be ${60}^o$ as shown in the figure. Find the height of the flag post.

Answer 1

Let $BX=xm$

In $\Delta ABC,$

$\tan \left(30°\right)=\frac{AB}{BC}$

$⟹\frac{1}{\sqrt{3}}=\frac{AB}{x+6}$

$⟹\frac{x+6}{\sqrt{3}}=AB$

In $\Delta ABX,$

$\tan \left(60°\right)=\frac{AB}{BX}$

$⟹\sqrt{3}=\frac{AB}{x}$

$⟹x\sqrt{3}=AB$

Equating both,

$x\sqrt{3}=\frac{x+6}{\sqrt{3}}$

$⟹3x=x+6$

$x=3m$

Thus, $AB=3\sqrt{3}m$