Philip P. answered • 03/05/14
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Sammy:
It takes two lines to make an angle, so your question is a bit confusing. Did you mean how many times a day does the minute hand make a right angle with the hour hand? If so, it makes two right angles with the hour hand every hour. Why? the minute hand makes one full 360 rotation wrt the hour hand every hour, and so it passes through all of the angles, including 90 degrees and 270 degrees wrt the hour hand every hour. Both 90 and 270 degrees are right angles. Since there are 24 hours in a day, that would be 48 right angles.
That's a different question than the one Vivian answered below, so please check and decide which question you need answered.
Philip P.
The period, or time it takes the minute hand to circle around and catch back up with the hour hand, is:
period = 65 minutes/60 minutes = 1.08
The number of cycles per hour then = 1/period = 1/1.08 = .923
The number of cycles in 24 hours, then = (0.923)(24) = 22.153. That's how you compute how many times the minute hand catches up the hour hand in 24 hours (round to 22).
Thanks for your question. I've learned something today as well!
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03/06/14
Philip P.
03/06/14