Question

The angle of depression of a car, standing on the ground from the top of a 75 mt
tower is 30°. Find the distance of the car from the foot of the tower in mts.
​

Answer 1

In right angle triangle ABC the ∠ACB=30°

(Angle of depression of a car) and the tower is 75 m high .

Let the distance of car from ground is x m

Then tan30° = AB = 75

BC x

⇒ 1 = 75

√3 x

⇒ x = 75√3 m

Answer 2

Answer :

• Distance of the car from the foot of the tower is 25√3 m.

Explanation :

Given :

• Angle of depression, θ = 30°
• Height of the tower, h = 75 m

To find :

• Distance of the car from the foot of the tower, b = ?

Knowledge required :

From the given figure, AB is the hypotenuse of the triangle, BC is the base of the triangle and AC is the height of the tower.

But we have to find the base of the triangle and we know that Height/base is tanθ.

So by using the tanθ, we can find the required value.

Solution :

By using tanθ and substituting the values in it, we get :

⠀⠀=> tanθ = P/B

⠀⠀=> tan30° = 75/B

⠀⠀=> 1/√3 = 75/B [tan30° = 1/√3]

⠀⠀=> B = 75/√3

By rationalising the equation, i.e, by multiplying (√3) to both the numerator and denominator, we get :

⠀⠀=> B = (75 × √3)/(√3 × √3)

⠀⠀=> B = 75√3/3

⠀⠀=> B = 25√3

⠀⠀⠀⠀⠀∴ B = 25√3

Therefore,

• Distance of the car from the foot of the tower, b = 25√3 m