A car is moving at uniform speed towards a tower It takes 15 minutes for the angle of depression fro...........

Quantitative Aptitude ( CCS) Trignometry

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?

6 min

6.5 min

7 min

7.5 min

छोटे Courses बड़े Results

Master Trignometry

Prepare through Micro-courses

Try Now

Explanation:

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.
Height & Distances
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.