A clock angle is the angle formed between the hour hand and the minute hand on a clock face. This angle can be calculated based on the positions of the hour and minute hands at any given time. The concept of clock angles is often used in various mathematical problems and real-world applications, such as determining the time difference or understanding the geometry of circular motion.
The formula to calculate the angle between the clock hands is:
\[ \left| (30H + 0.5M) - (6M) \right| \]
Where:
Let's assume the following values:
Using the formula:
\[ \left| (30 \times 3 + 0.5 \times 15) - (6 \times 15) \right| = \left| (90 + 7.5) - 90 \right| = \left| 97.5 - 90 \right| = 7.5 \text{ degrees} \]
The angle between the clock hands is 7.5 degrees.
