Asked by Lucille Fillinger
Zack looks at the clock and sees the hands have made a 90° angle. He realizes he has 2 hours before basketball practice starts. Which could be the angle formed by the hands of the clock when practice starts?
(1 point)
Responses
180°
180°
60°
60°
30°
30°
150°
150°
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Answers
Answered by
GPT-4o mini
When the clock hands form a 90° angle, we can find the possible angles that may form when 2 hours pass.
Initially, let’s understand how the clock hands move:
- The minute hand moves 360° in 60 minutes (6° per minute).
- The hour hand moves 360° in 12 hours (30° per hour).
In 2 hours, the minute hand moves:
- 2 hours = 120 minutes
- Movement = 120 minutes * 6°/minute = 720°
The hour hand moves:
- 2 hours = 2 * 30° = 60°
After 2 hours, the positions of the hands will be:
- Minute hand: 720° mod 360° = 0° (pointing at 12)
- Hour hand: 60°
The angle between them:
- The angle is the difference = |0° - 60°| = 60°.
To answer the question, at the start of basketball practice, the angle formed by the hands of the clock can be 60°.
So, the answer is **60°**.
Initially, let’s understand how the clock hands move:
- The minute hand moves 360° in 60 minutes (6° per minute).
- The hour hand moves 360° in 12 hours (30° per hour).
In 2 hours, the minute hand moves:
- 2 hours = 120 minutes
- Movement = 120 minutes * 6°/minute = 720°
The hour hand moves:
- 2 hours = 2 * 30° = 60°
After 2 hours, the positions of the hands will be:
- Minute hand: 720° mod 360° = 0° (pointing at 12)
- Hour hand: 60°
The angle between them:
- The angle is the difference = |0° - 60°| = 60°.
To answer the question, at the start of basketball practice, the angle formed by the hands of the clock can be 60°.
So, the answer is **60°**.