If a clock shows 9:15, what is the angle between the hour and minute hands?

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What’s inside this PDF?

Question: If a clock shows 9:15, what is the angle between the hour and minute hands?

Options:

112.5 degrees
90 degrees
135 degrees
75 degrees

Correct Answer: 112.5 degrees

Solution:

At 9:15, the hour hand is at 97.5 degrees (9*30 + 15*0.5) and the minute hand is at 90 degrees (15*6). The angle between them is |97.5 - 90| = 7.5 degrees.

If a clock shows 9:15, what is the angle between the hour and minute hands?

Practice Questions

If a clock shows 9:15, what is the angle between the hour and minute hands?

112.5 degrees
90 degrees
135 degrees
75 degrees

Questions & Step-by-Step Solutions

If a clock shows 9:15, what is the angle between the hour and minute hands?

Step 1: Understand that the clock has two hands: the hour hand and the minute hand.
Step 2: Know that each hour on the clock represents 30 degrees (360 degrees / 12 hours).
Step 3: Calculate the position of the hour hand at 9:15. The hour hand is at 9 hours and 15 minutes.
Step 4: Calculate the degrees for the hour hand: 9 hours * 30 degrees = 270 degrees.
Step 5: The hour hand also moves as the minutes pass. For 15 minutes, it moves an additional 0.5 degrees per minute (30 degrees / 60 minutes).
Step 6: Calculate the additional movement of the hour hand: 15 minutes * 0.5 degrees = 7.5 degrees.
Step 7: Add the two results for the hour hand: 270 degrees + 7.5 degrees = 277.5 degrees.
Step 8: Now calculate the position of the minute hand. Each minute represents 6 degrees (360 degrees / 60 minutes).
Step 9: Calculate the degrees for the minute hand at 15 minutes: 15 minutes * 6 degrees = 90 degrees.
Step 10: Find the angle between the hour and minute hands by taking the absolute difference: |277.5 degrees - 90 degrees|.
Step 11: Calculate the difference: 277.5 degrees - 90 degrees = 187.5 degrees.
Step 12: Since angles on a clock can be measured in both directions, we can also find the smaller angle: 360 degrees - 187.5 degrees = 172.5 degrees.
Step 13: The final answer is the smaller angle, which is 7.5 degrees.

Clock Angles – Understanding how to calculate the angles between the hour and minute hands of a clock based on their positions.
Time Conversion – Converting time into degrees for both hour and minute hands using the formulas: hour hand = hours * 30 + minutes * 0.5 and minute hand = minutes * 6.

If a clock shows 9:15, what is the angle between the hour and minute hands?

What’s inside this PDF?

If a clock shows 9:15, what is the angle between the hour and minute hands?

Practice Questions

Questions & Step-by-Step Solutions

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