Solution:
Consider PQ as the tower = h
XQ = YR = y
XY = 40 m
PR = h – 40
In right triangle PXQ
tan θ = PQ/XQ
Substituting the values
tan 600 = h/y
So we get
√3 = h/y
y = h/√3 ….. (1)
In right triangle PYR
tan θ = PR/YR
Substituting the values
tan 450 = (h – 40)/ y
So we get
1 = (h – 40)/ y
y = h – 40 …… (2)
Using both the equations
h – 40 = h/√3
By further calculation
√3h – 40√3 = h
√3h – h = 40√3
So we get
(1.732 – 1)h = 40 (1.732)
732h = 69.280
By division
h = 69.280/0.732 = 69280/732 = 94.64
Here
Height of the tower = 94.64 m = 95 m
Distance XQ = h – y = 95 – 40 = 55 m