Question

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Answer 1

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Step-by-step explanation:

GIVEN :-

The time in a clock is 12:30.

TO FIND :-

The radian measure of the angle between the minute hand of a clock and the hour hand when the time is 12:30.

SOLUTION :-

We know,

The angle in between each hour can be calculated as:- 360/12 = 30°

So, at 12:30, the hour hand will be between 12 and 1, and the minute hand will be at 6.

Now,

30 minutes = 1/2 hour

So, it means that the hour's hand has travelled = 30/2 = 15° beyond 12.

Difference of hours between the hour hand and the minute hand at 12:30 is 6 hrs.

So, the angle in between 12 (hour) and 30 (minutes at 6) is = 30 x 6 + 15 = 180 + 15 = 195°

We know,

Radian = (π/180)*degree

⇒Radian = (π/180)*195

⇒Radian = 13π/12

∴ So, the radian measure of the angle between the minute hand of a clock and the hour hand at 12:30 is 13π/12 radians.

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