Question

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

• A. 0°
• B. 7.5°
• C. 30°
• D. 22.5°

Hint:

Use formula \(\theta = |30H - \frac{11}{2}M|\) to find angle between hour and minute hands.

Answer 1

The Correct Option is B

Angle between hour and minute hand at any time can be calculated by: \[ \theta = \left| 30H - \frac{11}{2}M \right| \] where \(H\) = hour, \(M\) = minutes. Given \(H = 3\), \(M = 15\): \[ \theta = |30 \times 3 - \frac{11}{2} \times 15| = |90 - 82.5| = 7.5^\circ \] So, the angle between hour and minute hand at 3:15 is \(7.5^\circ\).

Final answer Answer: \(\boxed{7.5^\circ}\)