The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45°. If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60°, then find the height of the flagstaff. [Use √3=1.73]

Let AB is the tower of height h meter and AC is flagstaff of height x meter.
∠APB=45° and ∠BPC=60°
tan60° = (x+h)/120
√3 = (x+h)/120
x = 120√3 - h
tan45° = h/120
1 = h/120
h = 120
Substitute the value of h in x,
x = 120√3 - 120
x = 120(√3 - 1)
x = 120(1.73 - 1)
x = 87.6m
Therefore the height of the flagstaff = 87.6m