Question

The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building​

Answer 1

Answer:If the angle of elevation of the top of a tower from a point on the ground, which is 30m away from the foot of the tower, is 30°, then the height of the tower is 10√3 m.

Step-by-step explanation:Let us consider the height of the tower as AB, the distance between the foot of the tower to the point on the ground as BC.

In ΔABC, trigonometric ratio involving AB, BC and ∠C is tan θ.

tan C = AB/BC

tan 30° = AB/30

1/√3 = AB/30

AB = 30/√3

= (30 × √3) / (√3 × √3)

= (30√3)/3

= 10√3

Height of tower AB = 10√3 m.