Question

the angle of elavation of the top of the tower from a point A on the ground is 30 degree. on moving a distance of 20 meteres towards the foot of the tower to a point B the angle of elavation increaces to 60 degree. find the height of the tower and the distance of the tower from the point A

Answer 1

In rt angle ΔAQR, right angle at Q,
let QR=x metre be the height of the tower and let AB= 20merte
Also take BQ=y meter.
 tan60°=x/y=√3
x=y√3
tan30°=x/(y+20)=1/√3
sub 1 in 2,
y+20=x√3
       =y√3.√3
       =3y
   2y=20
     y=10m
     x=10√3
       =17.732m
Hence the height of the tower=17.32metres
     The distance from the point A to the tower=30metres