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: Calculate the minute hand angle from 12 o’clock. 
At 30 minutes, the minute hand is at: \[ 30 \times 6 = 180^{\circ}, \] since each minute corresponds to \(6^{\circ}\). 
Step 2: Calculate the hour hand angle from 12 o’clock. 
At 3:00, the hour hand is at \( 3 \times 30 = 90^{\circ} \). 
In 30 minutes, the hour hand moves further: 
\[ \frac{30}{60} \times 30 = 15^{\circ}. \] So, at 3:30, hour hand angle is: \[ 90^{\circ} + 15^{\circ} = 105^{\circ}. \] Step 3: Calculate the angle between the two hands.
Difference between hour and minute hands: \[ |105^{\circ} - 180^{\circ}| = 75^{\circ}. \] Since this is less than \(180^{\circ}\), it is the required angle.