Given Data

1. Time interval: Between 2 o'clock and 3 o'clock.
2. Target angle: 90 degrees.

Question

At what time between 2 and 3 o'clock are the hands of a clock at right angles?

Answer

27 3/11 minutes past 2.

Solution

1. Set up the clock angle formula: |30H - 5.5M| = 90.
2. Substitute H = 2: |30(2) - 5.5M| = 90 => |60 - 5.5M| = 90.
3. Solving 5.5M - 60 = 90 gives 5.5M = 150.
4. M = 150 / 5.5 = 300 / 11 = 27 3/11 minutes.
5. Therefore, the hands form a right angle at 27 3/11 minutes past 2.