Question

What is the angle between the hour and minute hand at 3:30?

• A. \(60^{\circ}\)
• B. \(75^{\circ}\)
• C. \(90^{\circ}\)
• D. \(105^{\circ}\)

Hint:

- Minute hand moves \(6^{\circ}\) per minute. - Hour hand moves \(0.5^{\circ}\) per minute (30 degrees per hour). - Angle between hands = absolute difference of their positions.

Answer 1

The Correct Option is B

Step 1: Minute hand angle calculation. The minute hand is at \( 30 \times 6 = 180^{\circ} \) from 12 o’clock, as each minute represents \(6^{\circ}\).
Step 2: Hour hand angle calculation. At 3:00, the hour hand is at \( 3 \times 30 = 90^{\circ} \). In 30 minutes, it moves an additional \( \frac{30}{60} \times 30 = 15^{\circ} \). Therefore, at 3:30, the hour hand’s angle is \( 90^{\circ} + 15^{\circ} = 105^{\circ} \) from 12 o’clock.
Step 3: Angle between hands. The difference between the hour and minute hands is \( |105^{\circ} - 180^{\circ}| = 75^{\circ} \). As this is less than \(180^{\circ}\), it is the correct angle.