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

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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) About Me  (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

abs%28%28150+%2B+x%2F2%29+-+6x%29+=+90

abs%28150+-+11x%2F2%29+=+90

150+-+11x%2F2+=+90 or 150+-+11x%2F2+=+-90

x+=+120%2F11+=+10.909 or x+=+480%2F11+=+43.636

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