What angle is formed between the hour and minute hand of a clock showing 3:15?

To determine the angle between the hour and minute hand of a clock at 3:15, we can break down the positions of both hands.

First, consider the minute hand. At 15 minutes past the hour, the minute hand is at the 3 on the clock face. Each number on the clock represents 30 degrees (360 degrees total divided by 12 numbers). Thus, at 15 minutes, the minute hand is at 90 degrees from the 12 o'clock position (15 minutes × 6 degrees, as each minute represents 6 degrees).

Next, consider the hour hand. At 3:00, the hour hand would be exactly at the 3, or 90 degrees. However, since it’s 15 minutes past 3, the hour hand has moved further. The hour hand moves at 0.5 degrees per minute (30 degrees per hour divided by 60 minutes). Therefore, in 15 minutes, the hour hand has moved an additional 7.5 degrees (15 minutes × 0.5 degrees).

Adding this to the initial position of the hour hand at 3:00 gives us: 90 degrees (for 3:00) + 7.5 degrees = 97