SOLUTION: At what time(s) between 5 and 6 o'clock will the hour and the minute hands be at right angles?

Question 395514: At what time(s) between 5 and 6 o'clock will the hour and the minute hands be at right angles?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
We can assign 12:00 as 0 degrees, 1:00 as 30 degrees, etc.

If the time is 5 hours and x minutes after 5:00, then the angle formed by the minute hand is (x/60)(360) = 6x (degrees). For each minute after 5, the hour hand moves 1/2 degree, so the hour hand has an angle of 150 + x/2. The angle between them is 90 degrees, so

or

or

Therefore the angle between the hands is 90 at roughly 5:11 and 5:44.
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