Question

Чему равен угол между минутной и часовой стрелками на часах, когда они показывают 9 часов 30 минут. Известно что 105 градусам но как это решить?

Answer 1

За 1 час часовая стрелка поворачивается на
360° : 12 час = 30°
За 30 минут - на 15°
В 9 ч 30 мин = 90° + 15° = 105° - ОТВЕТ

Answer 2

Calculating the Angle Between the Hour and Minute Hands of a Clock

To calculate the angle between the minute and hour hands of a clock when the time is 9:30, we can use the following approach:

1. Calculate the Angle for the Hour Hand: - The hour hand moves 360 degrees in 12 hours. - In 9 hours, it moves \( \frac{360}{12} \times 9 = 270 \) degrees. - For the additional 30 minutes, it moves \( \frac{30}{60} \times \frac{360}{12} = 15 \) degrees. - Therefore, the angle for the hour hand at 9:30 is \( 270 + 15 = 285 \) degrees.

2. Calculate the Angle for the Minute Hand: - The minute hand moves 360 degrees in 60 minutes. - At 30 minutes, it moves \( \frac{30}{60} \times 360 = 180 \) degrees.

3. Find the Difference: - The angle between the hour and minute hands is the absolute difference between the two angles. - \( |285 - 180| = 105 \) degrees.

Therefore, the angle between the minute and hour hands of the clock at 9:30 is 105 degrees.