Question

The angle of elevation of the top of a tower from a point A on the ground is ${30}^o$. On moving a distance of 20 metres towards the foot of the tower to a point B the angle of elevation increase to ${60}^o$. Find the height of the tower and the distance of the tower from the point A.

Answer 1

Let the Height of the tower be $CD$

In $△BCD,$

$\tan {60}^o=\frac{CD}{DB}$

$\Rightarrow CD=DB\sqrt{3}...........\left(1\right)$

In $△ACD,$

$\tan {30}^o=\frac{CD}{AD}$

$\Rightarrow AD=CD\sqrt{3}............\left(2\right)$

Also, it is given that $AB=20m=AD-BD$ ................. (3)

Using (1) and (2) in eq. (3) we get,

$\Rightarrow CD\sqrt{3}-\frac{CD}{\sqrt{3}}=20$

$\Rightarrow 2CD=20\sqrt{3}$

$\Rightarrow CD=\frac{20}{2}\sqrt{3}=17.32m$

$\Rightarrow$$AD=CD\sqrt{3}=17.32\times 1.732=30m$