You work every saturday from 9:00 a.m. to 5:00 p.m. find the measure of the angle generated by the hour hand of a clock during this time in both degrees and radians. compare this angle with the angle generated by the minute hand from 9:00 a.m. to 5:00 p.m.

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.

How to get the angle generated?

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

What is the angle generated by the minute hand?

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