Question

What is the angle between the minute hand and hour hand of a clock at half past two?

Answer 1

the time is usually based on 12-hour clock. A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or0.5° per minute.

Answer 2

The area which will be covered is this:

12  is 6/12 = 1/12

Now we will try to find the angle which is covered by a minute hand:

1/2 × 2π = π

and at the half past four the portion which will be covered is 12  is 4.5/12 = 3/8

Now the angle covered by the hour hand:

12  is 3/8 × 2 π = 3π/4

Now the angle at the minute hand, hour hand and half past four is

π−3π/4=π/4