Question

How many times will the minute band and the hour hand of a clock make a right angle from tipm to 5p.m?​

Answer 1

Answer:

At 2:x the angle between the hour and the minute had is 90 deg.

Or -2*30 + 5.5x = 90, or

5.5x = 90+60 = 150, or

x = 150/5.5 = 27.27. Or at 2:27:16.36 is the angle 90 deg.

30*30–5.5x = 90, or

5.5x = 90–90 = 0. Or at 3:00:00 is the angle 90 deg.

Or -3*30 + 5.5x = 90, or

5.5x = 90+90 = 180, or

x = 180/5.5 = 32.72. Or at 3:32:43.63 is the angle 90 deg.

Or -4*30 + 5.5x = 90, or

5.5x = 90+120 = 210, or

x = 210/5.5 = 38.18. Or at 4:38:10.91 is the angle 90 deg.

So at 2:27:16.36, 3:00:00, 3:32:43.63 and 4:38:10.91 is the angle 90 deg.

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Answer 2

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At 2:x the angle between the hour and the minute had is 90 deg.

Or -2*30 + 5.5x = 90, or

5.5x = 90+60 = 150, or

x = 150/5.5 = 27.27. Or at 2:27:16.36 is the angle 90 deg.

30*30–5.5x = 90, or

5.5x = 90–90 = 0. Or at 3:00:00 is the angle 90 deg.

Or -3*30 + 5.5x = 90, or

5.5x = 90+90 = 180, or

x = 180/5.5 = 32.72. Or at 3:32:43.63 is the angle 90 deg.

Or -4*30 + 5.5x = 90, or

5.5x = 90+120 = 210, or

x = 210/5.5 = 38.18. Or at 4:38:10.91 is the angle 90 deg.

So at 2:27:16.36, 3:00:00, 3:32:43.63 and 4:38:10.91 is the angle 90 deg.

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