Question

the angles of depression of the top and the bottom of a 7metre tall building from the top of a tower are 45 degree and 60 degree respectively .find the height of the tower in metres

Answer 1

let AB= height of tower
CD=height of building=7mts
CD=BE=7mts
DE=BC
From ∆ADE,
tan 45°=AE/DE
1=h-7/DE
DE=h-7 mts-----------1
From ∆ABC,
tan 60°=AB/BC
√3=h/BC
BC=h/√3 mts---------2
from 1 and 2
DE = BC
h-7=h/√3
h=√3(h-7)
h=h√3-7√3
h√3-h=7√3
h(√3-1)=7√3
h=7√3/√3-1
h=(7√3/√3-1)×(√3+1/√3+1)
h=(7√3×√3 + 7√3)/(√3×√3-1×1)
h=21+7×1.732/3-1
h=21+12.124/2
h=33.124/2
h=16.562
therefore height of tower = 16.562mts