A car is moving at uniform speed towards a tower. It takes 15 minutes for the angle of depression from the top of tower to the car to change from 300 to 600. What time after this, the car will reach the base of the tower?
Let AB is the tower of height x m. Let C and D be the points on the ground where the angles of depression are 300 and 600 respectively. It took the car 15 minutes to go from C to D.
In Δ ABD, tan 600 = AB/AD ⇒ √3 = x/AD ⇒ AD = x/√3 m
Again in Δ BAC,
tan 300 = x/AC ⇒ 1/√3 = x/AC ⇒ AC = √3x m
Now CD = AC – AD
CD = √3x – x/√3 = 2x/√3 m.
Now the car covered 2x/√3 m in 15 minutes
So it will cover AD = x/√m in 15 × √3/2x × x/√3 = 7.5 minutes.