Question

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

Answer 1

Hi____

i have to give a formulas for solving this type of problem

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Q(hours)=.5x(60*hours+minutes )
Q(minutes )=6xminutes
the angle Q=|Q(hours)-Q(minutes )|

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now in your question
4 hours 00minutes

Q(hours)=.5*(60*4+00)=120

Q(minutes )=6*00=00

so Q=120-0=120

hence 4 o clock angle is 120 degree .

hope it help
=

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