The angle of depression of a car, standing on the ground, from the top of a 75 m tower, is 30°. The distance of the car from the base of the tower is:

Question: The angle of depression of a car, standing on the ground, from the top of a 75 m tower, is 30°. The distance of the car from the base of the tower is:

Solution:
AB is a tower and AB = 75 m
From A, the angle of depression of a car C
on the ground is 30°


Let distance BC = x

Now, in ΔACB,
tanθ = AB/BC
⇒ tan30° = 75/x
⇒ 1/√3 = 75/x
⇒ x = 75√3
∴ BC = 75√3 m