Multiple choice

At what time between 5:30 and 6:00 will the hands of a clock be at right angles?

  1. 43 5 11 minutes past 5

  2. 43 7 11 minutes past 5

  3. 40 minutes past 5

  4. 45 minutes past 5

  5. 42 minutes past 5
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B Correct answer
AI explanation

Using the right angle formula for clock hands, theta equals 11 times M divided by 2 minus 30 times H. At 5 o'clock, substituting H as 5 and theta as 90 degrees gives 11 times M divided by 2 minus 150 equals 90. Solving this equation yields 11 times M divided by 2 equals 240, so M equals 480 divided by 11, which is 43 and 7 divided by 11 minutes. The hands will therefore be at right angles at 43 and 7 divided by 11 minutes past 5.

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