The angle generated by the hour hand measures -270° or -4.71 radians, and we will see that the angle generated by the minute hand is 12 times the one generated by the hour hand.
Remember that in a complete rotation we have an angle of 360°, and in a complete rotation we have 12 hours, then there is a relation:
12 hours = 360°
1 hour = 360°/12 = 30°
From 9:00 a.m to 5:00 p.m. there are 9 hours, so the angle that the hour hand does is:
A = 9*(30°) = -270°
(the negative sign is because this angle is measured clockwise)
Now we can write this in radians, remember that:
3.14 radians = 180°
Then:
1 = (3.14 rad/180°)
Then:
270° = -270°*(3.14 rad/180°) = -4.71 rad
Each hour that passes, the minute hand does a complete revolution. Then in 9 hours, the minute hand does an angle of:
A = 9*(-360°) = -3,240°
To compare this angle to the one generated by the minute hand we take the quotient:
-3,240°/-270° = 12
So this angle generated by the minute hand is 12 times the one generated by the hour hand.
If you want to learn more about angles, you can read:
https://brainly.com/question/14362353
