Question

a man on the top of he building observes a car at an angle of depression a , where tan a = 1/✓5 and sees that it is moving towards the base of the building. 10 minutes later , the angle of depression of the car is found at b = ✓5 . if the car moves with uniform speed, determine how much more time will it take to reach the base of the tower
​

Answer 1

Step-by-step explanation:

Let the tower be represented by CD, the initial position of the car by A and the second position of the car by B.

Let the distance travelled from A to B be d

1

in time t

1

and distance between B to C be d

2

in time t

2

.

In △DCB,tan45=

BC

CD

.

∴BC=CD=d

2

In △ACD,tan30=

AC

CD

∴

3

1

=

d

1

+d

2

d

2

∴d

1

+d

2

=

3

d

2

Since the speed of the car is uniform throughout its journey, we can say

t

1

+t

2

=

3

t

2

∴12+t

2

=

3

t

2

∴t

2

=16.39 min.