Question

the angle of elevation of the top of a tower from certain point is 30°.if the observer moves 20m towards the tower, the angle of elevation of the top increases 60°. find the height of the tower.​

Answer 1

✭ Refer to the attachment for diagram

In Δ ABD ,

$\implies \tt \tan(30) = \frac{h}{x}$

$\implies \tt \frac{1}{ \sqrt{3} } = \frac{h}{x}$

$\implies \tt x = \sqrt{3} h$

Now , in Δ ACD

$\implies \tt \tan(60) = \frac{h}{x - 20}$

$\implies \tt \sqrt{3} = \frac{h}{x - 20}$

$\implies \tt \sqrt{3} = \frac{h}{( \sqrt{3}h - 20) }$

$\implies \tt 3h - 20 \sqrt{3} = h$

$\implies \tt 2h = 20 \sqrt{3}$

$\implies \tt h = 10 \sqrt{3} \: m$

✭ The height of tower is 10√3 meter