Question

Choose the correct answer of the following question:

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 is

(a) $50\sqrt{3}$ m (b) $150\sqrt{3}$ m (c) $150\sqrt{2}$ m (d) 75 m [CBSE 2014]

Answer 1

Let AB be the tower and point C be the position of the car.

We have,

$$\begin{gathered} \mathrm{AB}=150\mathrm{m}\mathrm{and}\angle \mathrm{ACB}=30° \\ \mathrm{In}∆\mathrm{ABC}, \\ \tan 30°=\frac{\mathrm{AB}}{\mathrm{BC}} \\ \Rightarrow \frac{1}{\sqrt{3}}=\frac{150}{\mathrm{BC}} \\ \therefore \mathrm{BC}=150\sqrt{3}\mathrm{m} \end{gathered}$$

Hence, the correct answer is option (b).