If a clock shows 10:10, what is the angle between the hour and minute hands?

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Question: If a clock shows 10:10, what is the angle between the hour and minute hands?

Options:

Correct Answer: 75 degrees

Solution:

At 10:10, the hour hand is at 85 degrees (10*30 + 10*0.5) and the minute hand is at 60 degrees. The angle between them is |85 - 60| = 25 degrees.

If a clock shows 10:10, what is the angle between the hour and minute hands?

If a clock shows 10:10, what is the angle between the hour and minute hands?

Step 1: Understand that a clock has 12 hours and each hour represents 30 degrees (360 degrees / 12 hours).
Step 2: Calculate the position of the hour hand at 10:10. The hour hand moves 30 degrees for each hour and 0.5 degrees for each minute. So, for 10 hours, it is 10 * 30 = 300 degrees. For 10 minutes, it is 10 * 0.5 = 5 degrees. Therefore, the hour hand is at 300 + 5 = 305 degrees.
Step 3: Calculate the position of the minute hand at 10:10. The minute hand moves 6 degrees for each minute (360 degrees / 60 minutes). So, for 10 minutes, it is 10 * 6 = 60 degrees.
Step 4: Find the angle between the hour and minute hands. Subtract the smaller angle from the larger angle. The angle is |305 - 60| = 245 degrees.
Step 5: Since we want the smallest angle between the two hands, we take 360 - 245 = 115 degrees.

Clock Angle Calculation – Understanding how to calculate the angles of the hour and minute hands based on their positions.
Time Representation – Interpreting the time shown on a clock and converting it into degrees for both hands.