Find the exact angle measure between the minute and the hour hands at 1:15 p.m.
The hour hand turns one complete revolution or 360° in 12 hours, which is
360°/12 or 30° per hour.
At 12:00 both hands are upward vertically. At 1:00 the hour hand is 30°
from the vertical (and 60° from the horizontal).
In the 1/4 an hour (15 minutes) from 1:00 to 1:15, the hour hand has swung
through 1/4 of 30° or 7.5°, so at 1:15 the hour hand has moved 7.5° more from
the vertical, so it's 30°+7.5° or 37.5° from the vertical and 52.5° from the
horizontal, and the minute hand is exactly horizontal at 1:15, so the answer is
52.5°.
Edwin
