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The first right angle after two o'clock

clocksanglesalgebra

At exactly 2:00 the hands of a clock are 60 degrees apart, with the minute hand behind the hour hand.

At what time after 2:00 do the hands first form a right angle (90 degrees)? Give the number of minutes past two exactly, as a fraction, and to the nearest second.

Many people guess "a few minutes past two". Check that guess before you commit to it.

Show a hint

Track the angle between the hands minute by minute. It starts at 60 and shrinks, because the minute hand is catching up. Does it ever reach 90 before the hands overlap?

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