Trigonometry question....help please?

Question

Okay here is the problem anyone that can help explain it with the correct answer will get 10 points...Thanks

Here is the problem: Find the size of the angles in decimal degrees for the clock hand moving for the given time period for a twelve-hour clock. Answer should be exact.

a. hour hand in 4 hours
b. minute hand in 15 minutes
c. second hand in 55 seconds
d. hour hand in 45 mintues
e. second hand in 2 hours

Answer 1

a. hour hand in 4 hours: 4*(360/12) = 4*30 = 120

b minutes hand in 15 minutes: 15*(360/60) = 15*6 = 90

c. second hand in 55 seconds: 55*(360/60) = 55*6 = 330

d. hour hand in 45 minutes: 45 minutes = 3/4 of an hour
The angle is 3/4 * (360/12) = 3/4 * 30 = 90/4 = 22.5

e. 2 hours = 2*60*60 = 7200 seconds
7200 = 20*360, the angle is 0 degrees.

Answer 2

There are 12 numbers on a clock face, so the angle between any two consecutive numbers is 360/12 = 30 degrees. The hour hand moves 30 degrees in one hour (or 60 minutes, or 3600 seconds). The minute hand would take 5 minutes (or 1/12 of an hour, or 300 seconds) to move 30 degrees. And the second hand would take 5 seconds to move 30 degrees.

You should be able to calculate the values from these.

Answer 3

Once you realize that the hour hand goes 360 degrees in twelve hours, the minute hand does so in one hour, and the second hand does so in one minute, all of these can be easily solved with nothing more than multiplication and division.