Q14 of 61 Page 215

A straight highway leads to the foot of a tower. A man standing on the top of the tower spots a van at an angle of depression of 30°. The van is approaching the tower with a uniform speed. After 6 minutes, the angle of depression of the van is found to be 60°. How many more minutes will it take for the van to reach the tower?


Given, time taken by van to reach D from C = 6 minutes.


And let the speed = x


We know,


Distance = speed × time


⇒ Distance between D and C = DC = 6x


In triangle ACB,


∠ACB = ∠ OAC (alternate angles are equal)


= 30°


Also,






……… (1)


Now, in triangle ABD,


∠ABD = ∠ OAD (alternate angles are equal)


= 60°


We know,





AB = BD√3 ……… (2)


Now, equating (1) & (2), we get–



⇒ BD + 6x = BD × 3


⇒ 2BD = 6x



⇒ BD = 3x (where, x is speed)


Now, comparing it with Distance = speed × time, we have–


Time = 3 minutes.


Hence, it take 3 minutes more for the van to reach the tower.


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