The depression of a car parked on the road from the top of a 150 high tower is 30°. The distance of the car from the tower (in metres) is :

The height of the tower () = 150 The angle of depression = 30°∠ = ∠ [alternate angles]Let the distance of the car from tower = ‘’ In triangle ABC, tan 30° = ACAB13=150×xx=1503mThe distance of the car from the tower is 1503 mHence, option (b) is correct.

The depression of a car parked on the road from the top of a 150 high tower is 30°. The distance of the car from the tower (in metres) is :

The height of the tower () = 150 The angle of depression = 30°∠ = ∠ [alternate angles]Let the distance of the car from tower = ‘’ In triangle ABC, tan 30° = ACAB13=150×xx=1503mThe distance of the car from the tower is 1503 mHence, option (b) is correct.

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The depression of a car parked on the road from the top of a 150 𝑚 high tower is 30°. The distance of the car from the tower (in metres) is :

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$50 \sqrt{3}$

$150 \sqrt{2}$

$150 \sqrt{3}$

answer is B.

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Detailed Solution

The height of the tower (𝐴𝐶) = 150 𝑚
The angle of depression = 30°
∠𝐷𝐶𝐵 = ∠𝐴𝐵𝐶 [alternate angles]
Let the distance of the car from tower 𝐴𝐵 = ‘𝑥’ 𝑚
In triangle ABC, tan 30° = $\frac{A C}{A B}$
$\begin{aligned} \frac{1}{\sqrt{3}} = 150 \times x \\ x = 150 \sqrt{3} m \end{aligned}$
The distance of the car from the tower is $150 \sqrt{3}$ m
Hence, option (b) is correct.