What is the exact angle between the minute and hour hand at 7:45 pm?

Question

What is the exact angle between the minute and hour hand at 7:45 pm?

Answer 1

The clock is round, hence the total angle is 360 degrees.

Between any two consecutive hours (eg 3:00 and 4:00), the angle is equal to 360 degrees / 12 = 30 degrees.

At 7:45 the hour hand has gone past 7, so that accounts for 7 x 30 degrees = 210 degrees.  At 7:45 it has gone 3/4 of the way between 7:00 and 8:00 and that is (3/4) x 30 degrees = 22.5 degrees.  Adding that to the 210 degrees, we know that the hour hand is at 232.5 degrees.

Meanwhile the minute hand has gone 3/4 of the way around the clock so its angle is (3/4) x 360 degrees = 270 degrees.

The difference between 270 degrees and 232.5 degrees is =

270 - 232.5 = 37.5 degrees.   <<<<<  Final Answer

Answer 2

30º between every hour

so there are 30º between the minute hand at 9 and 8

the hour hand has gone 3/4 of the way between 7 and 8.

1/4 to go, so

30º + 30(1/4) = 37.5º

Answer 3

The hour hand is at 7/12ths of a circle.

The minute hand is 3/4 of the way around (45 minutes).  If you multiple the top and bottom of 3/4 by 3, you get 9/12.  In other words, the minute hand is 9/12th of the way around the circle.

If we take the difference between the two hand positions, we have 9/12 - 7/12 = 2/12.  So the angle between the two hands is 2/12th of a circle.  Simplifying that, we have 1/6th.

There are 360 degrees in a circle, so in degree terms, the angle between the hands is given by:

360 x 1/6

That's 60 degrees.

Answer 4

right angle 45 degrees

Answer 5

minute hand is at 270degrees

hour hand is at 210+30(45/60)=232.5

subtract them and you get 37.5 degrees

make it a good day

Answer 6

There are 360 degrees in any circle including a clock's face.  There are 60 minutes on the clock to 360/60=6 degrees between each minute. The 7 lies at 35 minutes thus it is at the 210 degree position. The minute hand is on the 9 so that is equal to 45 munutes which is also 270 degrees.  Subtract 210 degrees from 270 degrees and you get the difference of 60 degrees which is the number of degrees between the two hands.

Answer 7

37.5 degrees