the angle of elevation of the top of a tower from certain point is 30�

1.	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» ✭ 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