Question

What angle will be traced by the hands of a clock at 7:35?

• A. \(7\frac {1}{2}\degree\)
• B. \(17\frac {1}{2}\degree\)
• C. \(27\frac {1}{2}\degree\)
• D. \(37\degree\)

Answer 1

The Correct Option is B

The problem involves calculating the angle between the hour and minute hand of a clock at 7:35. To do this, we follow these calculations:

Step 1: Calculate the minute hand's angle. Each minute indicates 6 degrees of rotation (since 360 degrees / 60 minutes = 6 degrees per minute). At 35 minutes, the angle is: \[35 \times 6 = 210\degree\]

Step 2: Calculate the hour hand's angle. Every hour represents 30 degrees (since 360 degrees / 12 hours = 30 degrees per hour). For 7 hours and 35 minutes: \[7 \times 30 + \left(\frac{35}{60} \times 30\right) = 210 + 17.5 = 227.5\degree\]

Step 3: Find the angle between the two hands. The angle between the hour and the minute hand is the absolute difference between their angles: \[|227.5 - 210| = 17.5\degree\]

Conclusion: The angle traced by the hands of the clock at 7:35 is \(17\frac{1}{2}\degree\).