Question

Find the angle between clock hands at 3:40 PM.

• A. 50\(^{\circ}\)
• B. 130\(^{\circ}\)
• C. 120\(^{\circ}\)
• D. 140\(^{\circ}\)

Hint:

Remember the speeds of the hands: the minute hand moves 6\(^{\circ}\) per minute, and the hour hand moves 0.5\(^{\circ}\) per minute. You can also calculate the position of each hand from the 12 o'clock mark and find the difference.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to calculate the angle between the hour hand and the minute hand of a clock at the specific time of 3:40 PM.
Step 2: Key Formula or Approach:
The angle (\(\theta\)) between the hour hand (H) and the minute hand (M) can be calculated using the formula: \[ \theta = \left| \frac{60H - 11M}{2} \right| \text{ or } \theta = \left| 30H - \frac{11}{2}M \right| \] Here, H is the hour (3) and M is the minutes (40).
Step 3: Detailed Explanation:
Using the formula with H = 3 and M = 40: \[ \theta = \left| 30(3) - \frac{11}{2}(40) \right| \] \[ \theta = \left| 90 - 11 \times 20 \right| \] \[ \theta = \left| 90 - 220 \right| \] \[ \theta = \left| -130 \right| \] \[ \theta = 130^{\circ} \] The angle between the clock hands is 130 degrees. If the result is greater than 180\(^{\circ}\), we take the reflex angle (360\(^{\circ}\) - \(\theta\)), but since 130\(^{\circ}\) is less than 180\(^{\circ}\), it is the correct answer.
Step 4: Final Answer:
The angle between the clock hands at 3:40 PM is 130\(^{\circ}\).