This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Calculate the angle of the minute hand from the 12 o'clock position. The minute hand moves 360^ in 60 minutes, which is 6^ per minute. At 15 minutes past the hour, the minute hand's angle is: Minute hand angle = 15 minutes × 6^/minute = 90^ Step 2: Calculate the angle of the hour hand from the 12 o'clock position. The hour hand moves 360^ in 12 hours, which is 30^ per hour. It also moves 0.5^ per minute (30^ / 60 minutes). At 3:15, the hour hand's angle is based on 3 full hours and 15 minutes: Hour hand angle = (3 hours × 30^/hour) + (15 minutes × 0.5^/minute) Hour hand angle = 90^ + 7.5^ = 97.5^ Step 3: Find the absolute difference between the angles of the two hands. The angle between the hour and minute hands is the absolute difference of their positions: Angle = |Hour hand angle - Minute hand angle| Angle = |97.5^ - 90^| = 7.5^ The angle between the hour and minute hands at 3:15 is 7.5^. 3 done, 2 left today. You're making progress.