Question

what is angle traced by the hour-hand in 23 minutes
​

Answer 1

Step-by-step explanation:

The easiest way to solve this kind of problem if you don't want to memorize formulas is just to figure out the angle of both hands and then subtract. I'll use the conventions that 12:00 is zero degrees and that positive angles are clockwise.

The minute hand angle is the easiest since an hour (i.e. 60 minutes) corresponds to the entire 360 degrees, each minute must correspond to 6 degrees. So just multiply the number of minutes in the time by 60 to get the number of degrees for the minute hand. In your problem, the answer is 180 degrees.

Next, you have to figure out the angle of the hour hand. Since there are 12 hours in the entire 360 degrees, each hour corresponds to 30 degrees. But unless the time is EXACTLY something o'clock, you have to write the time as a fractional number of hours rather than as hours and minutes. In your problem, the time is 8:30 which is 8+12=172 hours. Since each hour corresponds to 30 degrees, we multiply to get 172⋅30=255 degrees.

Since the hour hand is at 255 degrees and the minute hand is at 180 degrees, we can subtract to get the angle of separation. 255−180=75 degrees.

If you want the angle to always be between 0 and 180 degrees, you may sometimes need one extra step although you do not in this problem. For example, at 11:10, the minute hand is at (10)(6)=60 degrees while the hour hand is at (11+16)(30)=335 degrees. So the difference is 275 degrees. While this answer is correct, it doesn't follow the normal convention that angles of this type should be between 0 and 180 degrees. To get the more conventional answer, you should subtract the result from 360 to get 360−275=85 degrees.

Answer 2

The answer is 11.4°

GIVEN

Time = 23 minutes.

TO FIND

Angle traced by hour-hand in 23 minutes.

SOLUTION

We can simply solve the above problem as follows;

First, we will convert 23 minutes into hour

23 minutes = 23/60 = 0.38 hrs

Now,

We know that,

Angle made by an hour hand in 12 hours = 360°

So,

Angle made by the hour hand in 1 hour = 360/12 = 30°

Therefore,

Angle made by hour hand in 0.38 hours = 30 × 0.38 = 11.4°

Hence, The answer is 11.4°

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