A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 min for the angle of elevation to change from 45° to 60°. After how much more time will this car reach the base of the tower? Options: a. 5( √3+ 1 ) b. 6 (√3 +√2) c. 7 (√3- 1) d. 8 (√3-2)

The correct answer is option a.

a. 5( √3+ 1 )

Step-by-step explanation:

Given that the angle changes from 45° to 60° in 10 minutes.

This situation can be represented as right angled triangles ABC (in the starting when angle is 45°)and ABD (after 10 minutes when the angle is 60°).

AB is the tower (A be its top and B be its base).

Now, we need to find the time to be taken to cover the distance D to B.

First of all, let us consider ABC.

Using tangent property:

Using tangent property in ABD:

Now distance traveled in 10 minutes, CD  = BC - BD

Now, we can say that more distance to be traveled to reach the base of tower is BD i.e. ''

So, more time required = Distance left divided by Speed

So, The correct answer is option a.

a. 5( √3+ 1 )