What is the angle between the hour and minute hands of a clock when the time reads 3:15?
The angle between the hands of the clock is 0 degrees at 3:15. Let's calculate the angle between them. Since there are 12 numbers on the face of a clock, the angle between any two numbers is 360/12 = 30 degrees. Therefore, the minute hand, which is pointing towards 3, has traveled a distance of 15 minutes * 6 degrees per minute = 90 degrees from 12 to 3. The angle between the hands of the clock is given by the difference between the two angles: |hour hand angle - minute hand angle| = |(3 * 30 degrees) - (90 degrees)| = |90 degrees - 90 degrees| = 0 degrees.
Calculating the Angle Between a Clock's Two Hands at 3:15
Angle Formulas:
To determine the angle between the hour and minute hands of a clock at any given time, we need to apply some basic formulas and calculations. At 3:15, the hour hand is at 3, while the minute hand is at 15 minutes past the hour, i.e., at 3.
Minute Hand Angle Calculation:
The minute hand moves 360 degrees in 60 minutes, which means it moves 6 degrees per minute. At 3:15, the minute hand is pointing towards 3, which equates to a location of 15 minutes * 6 degrees per minute = 90 degrees from 12 to 3 on the clock face.
Hour Hand Angle Calculation:
Since there are 12 numbers on a clock face, each number represents 30 degrees (360 degrees / 12). At 3 o'clock, the hour hand is pointing directly at 3, which corresponds to 3 * 30 degrees = 90 degrees.
Calculating the Angle Between the Two Hands:
To find the angle between the hour and minute hands, we need to subtract the minute hand angle from the hour hand angle. This results in |90 degrees - 90 degrees| = 0 degrees.
In conclusion, at 3:15, the angle between the hour hand and minute hand of the clock is 0 degrees. This signifies that both hands are aligned and point in the same direction. Understanding how to calculate the angle between the hands of a clock at a specific time can help in visualizing time concepts and enhance problem-solving skills related to time and angles.