Question

A pole of height 5m is fixed on the top of the tower. The angle of elevation of the top of the pole as observed from a point A on the ground is 60° and the angle of depression of the point A from the top of the tower is 45°. Find the height of tower. Take root 3 ( 1.732)
Ans : 6.83

Answer 1

Please refer to the given figure,
Let the distance between Tower and point A be d
Let the height of tower be x
In ΔEBA,
tan 60° = EB/BA
√3 = 5+x/d
d = 5+x/√3
In ΔCDA,
CD = BA and DA = CB
tan 45° = DA/CB
1 = x/d
1 = x/5+x/√3
1 = √3x/5+x
5+x = √3x
5+x = 1.732x
0.732x = 5
x = 6.830m = 6.83m