https://file.aiquickdraw.com/mathbot/file/1726993972672xyby73st.jpg

The question asks to find the angle between the hour hand and the minute hand of a clock when the time is 3:25.

### Step-by-step solution:

1. **Minute hand angle:**
   The minute hand moves 360° in 60 minutes, so it moves 6° per minute. At 25 minutes, the minute hand will be at:
   \[
   25 \times 6 = 150^\circ
   \]
   from the 12 o'clock position.

2. **Hour hand angle:**
   The hour hand moves 360° in 12 hours, or 30° per hour (since 360° / 12 = 30°). At exactly 3:00, the hour hand would be at:
   \[
   3 \times 30 = 90^\circ
   \]
   But at 3:25, the hour hand has moved a bit further. It moves 0.5° per minute (since 30° in 60 minutes), so in 25 minutes, it will move:
   \[
   25 \times 0.5 = 12.5^\circ
   \]
   Therefore, at 3:25, the hour hand will be at:
   \[
   90^\circ + 12.5^\circ = 102.5^\circ
   \]

3. **Angle between the hands:**
   Now, the angle between the hour hand (102.5°) and the minute hand (150°) is:
   \[
   |150^\circ - 102.5^\circ| = 47.5^\circ
   \]

Thus, the angle between the hour and minute hand at 3:25 is **47.5 degrees**.

Would you like further details or have any questions?

Here are five related questions for practice:
1. What is the angle between the hands at 4:15?
2. Find the angle at 7:30.
3. What is the smaller angle between the hands at 6:00?
4. At what time between 2:00 and 3:00 will the angle between the hands be exactly 90°?
5. How does the movement of the hour hand affect the calculation?

**Tip:** Always remember that the clock's hour hand moves gradually between hour marks as the minutes pass!

Find the angle between the hour hand and the minute hand of a clock when the time is 3:25.

Discover how to calculate the angle between the hour hand and the minute hand of a clock at 3:25 with a clear step-by-step solution. This problem explores concepts in geometry and trigonometry using practical formulas for the movement of clock hands. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation