Question

find the angle between the hour hand and minute hand in circular measure at 4' o clock

Answer 1

Answer:

120°

Step-by-step explanation:

We know that 12 hours make 360° as it forms a circle. Then 1 hour must form ?

Using Ratio Method we get,

⇒ 12 : 360 :: 1 : ?

⇒ 12 × x = 360 × 1

⇒ 12x = 360

⇒ x = 360 / 12 = 30°

Hence 1 hour will have 30°.

Now for 4: 00 it is having 4 hours gap from 12.

Hence it will have 4 times of angle between 1 hour

⇒ 4 × ( Angle between one hour )

⇒ 4 × 30 = 120° which can also be written as 4π/3 degrees.

Hence it will have 120° between hour and minute hand.

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