Question

A clock shows the time as 3:15. What is the angle between the hour and minute hands?

• A. 0°
• B. 7.5°
• C. 30°
• D. 37.5°

Hint:

Use the clock angle formula \( |30H - 5.5M| \) for precision. Remember: minute hand moves 6° per minute, hour hand moves 0.5° per minute. Always take the smaller angle between the hands.

Answer 1

The Correct Option is B

To solve the problem, we need to calculate the angle between the hour and minute hands of the clock when the time is 3:15.

1. Understanding the Concepts:

- The clock has 12 hours, and the full circle is 360 degrees.
- Each hour mark represents \( \frac{360}{12} = 30 \) degrees.
- The minute hand moves 6 degrees per minute (\( \frac{360}{60} \)).
- The hour hand moves 0.5 degrees per minute (\( \frac{30}{60} \)).

2. Given Values:

- Time: 3:15
- Minute hand position: 15 minutes
- Hour hand position: 3 hours and 15 minutes

3. Calculating the Angles:

Minute hand angle:

The minute hand is at 15 minutes, so angle from 12 o’clock:

\[ 15 \times 6 = 90^\circ \]

Hour hand angle:

At 3:00, the hour hand is at \(3 \times 30 = 90^\circ\).
In 15 minutes, the hour hand moves further:

\[ 15 \times 0.5 = 7.5^\circ \]

Total hour hand angle:

\[ 90 + 7.5 = 97.5^\circ \]

4. Calculating the Angle Between the Two Hands:

Difference between angles:

\[ |97.5 - 90| = 7.5^\circ \]

The angle between the hour and minute hands is \(7.5^\circ\).

Final Answer:

The angle between the hour and minute hands at 3:15 is 7.5 degrees.