From 10 a.m. to 3:44 p.m.:
10 a.m. to 3 p.m. = 5 hours
3 p.m. to 3:44 p.m. = 44 minutes
Total time elapsed = 5 hours 44 minutes
The hour hand completes one full circle (360°) in 12 hours.
In 1 hour, the hour hand moves:
12360°=30°
In 1 minute, the hour hand moves:
6030°=0.5°
Angle traced in 5 hours:
5×30°=150°
Angle traced in 44 minutes:
44×0.5°=22°
Total angle traced:
150°+22°
=172°
Therefore, the angle traced by the hour hand is 172°.