From the top of hill 240 m high, the angles the angles of depression of the top and bottom of a pole are 30° and 60°, respectively. The difference (in m) between the height of the pole and its distance from the hill is:

A. 120(2 - √3)

B. 120(√3 - 1)

C. 80(√3 - 1)

D. 80(2 - √3)

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & 3 \to 240 \cr & \sqrt 3 \to \frac{{240}}{3} \times \sqrt 3 = 80\sqrt 3 \cr & {\text{Height of the pole}} \cr & = 160 - 80\sqrt 3 \cr & = 80\left( {2 - \sqrt 3 } \right) \cr} $$