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If a clock shows 3:15, what is the angle between the hour and the minute hands?

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Question: If a clock shows 3:15, what is the angle between the hour and the minute hands? (2023)

Options:

  1. 45 degrees
  2. 90 degrees
  3. 97.5 degrees
  4. 75 degrees

Correct Answer: 97.5 degrees

Exam Year: 2023

Solution: 

At 3:15, the hour hand is at 97.5 degrees (3*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 3:15, what is the angle between the hour and the minute hands?

Practice Questions

Q1
If a clock shows 3:15, what is the angle between the hour and the minute hands? (2023)
  1. 45 degrees
  2. 90 degrees
  3. 97.5 degrees
  4. 75 degrees

Questions & Step-by-Step Solutions

If a clock shows 3:15, what is the angle between the hour and the minute hands? (2023)
  • Step 1: Understand that the clock has 12 hours and each hour represents 30 degrees (360 degrees / 12 hours).
  • Step 2: Calculate the position of the hour hand. At 3:00, the hour hand is at 3 * 30 = 90 degrees.
  • Step 3: Since it's 3:15, the hour hand moves further. It moves 0.5 degrees for each minute (30 degrees / 60 minutes).
  • Step 4: Calculate the additional movement of the hour hand for 15 minutes: 15 * 0.5 = 7.5 degrees.
  • Step 5: Add the additional movement to the hour hand's position: 90 degrees + 7.5 degrees = 97.5 degrees.
  • Step 6: Calculate the position of the minute hand. At 15 minutes, the minute hand is at 15 * 6 = 90 degrees.
  • Step 7: Find the angle between the hour and minute hands by subtracting the smaller angle from the larger angle: 97.5 degrees - 90 degrees = 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.
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