Find the measure of the smaller angle formed by the hands of a clock at the following time.
3:15
The angle is
Answer
Final Answer: The measure of the smaller angle formed by the hands of a clock at 3:15 is \(\boxed{7.5}\) degrees.
Step 1 ：The minute hand of a clock moves 360° every hour, or 6° per minute. The hour hand moves 360° every 12 hours, or 0.5° per minute.
Step 2 ：At 3:15, the minute hand will be at the 3 o'clock position, and the hour hand will be 1/4 of the way between the 3 and the 4.
Step 3 ：Therefore, we need to calculate the difference in degrees between these two positions.
Step 4 ：Let's denote the position of the hour hand as \(hour\_position = 3.25\) and the position of the minute hand as \(minute\_position = 15\).
Step 5 ：The degree of the hour hand is \(hour\_degree = 97.5\) and the degree of the minute hand is \(minute\_degree = 90\).
Step 6 ：The angle between the two hands is \(angle = 7.5\).
Step 7 ：Since we are looking for the smaller angle, we find that \(smaller\_angle = 7.5\).
Step 8 ：Final Answer: The measure of the smaller angle formed by the hands of a clock at 3:15 is \(\boxed{7.5}\) degrees.
