### Angles formed by the hands of a clock - January 1996

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This month's project has three parts. Do your best to answer all of them, but feel free to send in partial answers. Explain your answers as well as you possibly can - many people send in correct answers each month with no explanations, and that's not going to win anything as long as I'm in charge around here. :-)
1. At how many different times will the hands of a clock make a right angle? At what times will this occur? Determine your answers to the nearest second.

2. Find a time at which the hands of a clock make a 45-degree angle. Generalize your method to find a time at which the hands of a clock form any given angle.

3. What angle will the hands of a clock form at 3:20? Do not use a protractor. Generalize your method to give the angle formed by the hands of a clock at any given time.

[My thanks to Gary Martin (gmartin@kimiyo.ed.hawaii.edu) for suggesting this project.]

- Annie Fetter