A vertical tower is surmountly by a vertical flagstaff of height H. At a point of on an aeroplane, the angle of elevation of the top of the tower is alpha and of the flagstaff is beta. prove that

H = Htan alpha /  tan beta - tan alpha                    

let height of tower from point level=h

let height of flag from top of tower be H

let distance between point and foot of tower be x

(h/x)=tana

(h+H)/x=tanb

(tanb/tana)=(H+h)/(h)

(tanb/tana)-1=H/h

(tanb-tana)/tana=H/h

h=Htana/(tanb-tana)