Find the angle traced by the hour hand of a correct clock between 10 a.m. and 3:44 p.m. on the same day.

172°

The correct answer is Option (3) → 172°

1. Calculate the Time Elapsed

From 10:00 a.m. to 3:44 p.m.:

• 10:00 a.m. to 3:00 p.m. = 5 hours
• 3:00 p.m. to 3:44 p.m. = 44 minutes
• Total Time = 5 hours 44 minutes

2. Determine the Speed of the Hour Hand

A clock is a circle of $360^\circ$. The hour hand completes one full rotation in 12 hours.

• Angle per hour = $\frac{360^\circ}{12} = 30^\circ$
• Angle per minute = $\frac{30^\circ}{60} = 0.5^\circ$

3. Calculate the Total Angle

• Angle for 5 hours = $5 \times 30^\circ = 150^\circ$
• Angle for 44 minutes = $44 \times 0.5^\circ = 22^\circ$
• Total Angle = $150^\circ + 22^\circ = 172^\circ$

Final Answer: The angle traced by the hour hand is 172°.