Question

What is the number of degrees in the smaller angle formed by the hour and minute hands of a clock at 5:44?

Answer 1

The hour hand of the clock moves 360 degrees in 12 hours.

The quantity of degrees the hour hand moves per hour is in this way 360/12 = 30 degrees.

The hour hand of the clock moves 360 degrees in 12 *60 = 720 minutes.

The quantity of degrees the hour hand moves every minute is accordingly 360/720 = 1/2 degrees.

So the hour hand moves 1/2 degree for each minute.

The minute hand moves 360 degrees in a one hour.

The quantity of degrees the minute hand moves every minute is accordingly 360/60 = 6 degrees.

At 5:44, the quantity of minutes the hour hand has moved is 5 * 60 + 44 = 344 minutes.

At a half degree for each minute, the hour hand has moved .5 * 344 = 172 degrees.

At 5:44, the quantity of minutes the minute hand has moved is 44 minutes.

At 6 degrees for each minute, the minute hand has moved 6 * 44 = 264 degrees.

The angle between the minute hand and the hour hand is along these lines 264 degrees minus 172 degrees = 92 degrees.

Since that angle is under the 180 degrees, it must be the littler edge between the hour hand the minute