Solution:
Consider TR as the tower where TR = h
BR = x
AB = 10 m
Angles of elevation from the top of the tower at A and B are 300 and 450
In right triangle TAR
tan θ = TR/AR
Substituting the values
tan 300 = h/ (10 + x)
So we get
1/√3 = h/ (10 + x)
h = (10 + x)/ √3 …. (1)
In triangle TBR
tan 450 = TR/BR = h/x
So we get
1 = h/x
x = h ….. (2)
Using both the equations
h = (10 + h)/ √3
√3h = 10 + h
By further calculation
√3h – h = 10
(1.732 – 1) h = 10
0.732 h = 10
h = 10/0.732 = 13.66
Hence, the height of the tower is 13.7 m.