Question

How many times do the hands of a clock make a 90 degree angle in 36 hours?

Answer 1

Answer:

At about 11 minutes to 1 o'clock. So every 24 hours there are 44 right angles between minute hand and second hand. The following C code prints out the times of the day (12hr cycle) that the hands make 90degree angles (to the nearest 3 seconds to avoid the need for floating point). It is indeed 44 times.

Answer 2

Answer:

The hands of a clock make a 90 degree angle in 36 hours 66 times.

Step-by-step explanation:

• If you use a rotating coordinate system with the hour hand fixed, the minute hand only makes 11 revolutions and is at right angles to the hour hand 22 times. 322=66 in 36 hours
• In one hour, the hands of the clock make 90° = 2 times; in 36 hours, the hands make 36*2 = 72 times.
• But now we need to look at the times when the angle was only made once. Those are total = 4+2 = 6 times, so our answer is 72-6 = 66 times.
• In other words, in order to achieve a 90-degree angle, the minute hand "overtakes" the hour hand 44 times in 24 hours. As a result, the answer to your question is 44, and HENCE in 36 hours, it will be 66.

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