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The angle of 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 meters) is.

A. $50 \sqrt{3}%$ B. $150 \sqrt{3}%$ C. $100 \sqrt{3}%$ D. 75 Answer: Option B
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Solution(By Apex Team)

The angle of depression of a car parked on the road. image Let AB be the tower of height 150 m C is car and angle of depression is 30° $\begin{array}{l}\therefore\ \angle\text{ACB}=30^{\circ}\ \text{Alternatre angle)}\\ \text{In right angled triangle}\ \triangle\text{ABC}\\ \frac{BC}{AB}=\cot30^{\circ}\\ \Rightarrow\frac{BC}{150 }=\sqrt{3}\\ \Rightarrow BC=150\sqrt{3}\text{m}\\ \end{array}$ That is, distance of the car from the tower is $150 \sqrt{3} m$