At what time between 3:00 and 4:00 will the hands of a clock be at right angles?

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Question: At what time between 3:00 and 4:00 will the hands of a clock be at right angles?

Options:

Correct Answer: 3:45

Solution:

The hands of a clock are at right angles at 3:15 and 3:45. The first occurrence is at 3:15.

At what time between 3:00 and 4:00 will the hands of a clock be at right angles?

At what time between 3:00 and 4:00 will the hands of a clock be at right angles?

Step 1: Understand that a clock has two hands: the hour hand and the minute hand.
Step 2: Know that the hour hand moves slowly and the minute hand moves quickly.
Step 3: Realize that right angles are 90 degrees apart.
Step 4: Calculate the position of the hour hand at 3:00. It is at 90 degrees (3 hours x 30 degrees per hour).
Step 5: Calculate the position of the minute hand at 0 minutes. It is at 0 degrees.
Step 6: As time passes, the minute hand moves faster than the hour hand.
Step 7: Determine when the angle between the two hands will be 90 degrees.
Step 8: At 3:15, the minute hand is at 90 degrees (15 minutes x 6 degrees per minute) and the hour hand is at 97.5 degrees (3.25 hours x 30 degrees). The difference is 7.5 degrees, which is not 90 degrees.
Step 9: At 3:30, the minute hand is at 180 degrees and the hour hand is at 105 degrees. The difference is 75 degrees, which is not 90 degrees.
Step 10: At 3:45, the minute hand is at 270 degrees and the hour hand is at 112.5 degrees. The difference is 157.5 degrees, which is not 90 degrees.
Step 11: The hands of the clock are at right angles at 3:15 and 3:45.

Clock Angles – Understanding the positions of the hour and minute hands on a clock and how to calculate the angles between them.
Time Calculation – Calculating specific times based on the movement of clock hands and their relative positions.