Math Problem Statement
Solution
The question in the image is in Gujarati and translates to:
"At 5:30, what angle is formed between the hour hand and the minute hand of the clock?"
Let's solve this.
Step-by-step explanation:
-
Hour hand movement:
- The hour hand moves 30 degrees for every hour (360°/12 hours).
- At 5:30, the hour hand is halfway between 5 and 6, so its position is: So, the hour hand is at 165 degrees from the 12 o'clock position.
-
Minute hand movement:
- The minute hand moves 6 degrees per minute (360°/60 minutes).
- At 30 minutes, the minute hand is at: So, the minute hand is at 180 degrees from the 12 o'clock position.
-
Angle between the hour and minute hand:
- The angle between the two hands is the difference between their positions:
Thus, the angle between the hour hand and the minute hand at 5:30 is 15 degrees.
The correct answer is option D) 15°.
Let me know if you need further details!
Here are five related questions to expand on this:
- What is the angle between the hands of the clock at 4:20?
- How many degrees does the hour hand move per minute?
- What is the smallest angle between the hands of a clock at 3:15?
- How can we calculate the angle if the time is not exact, such as 7:45?
- What is the reflex angle between the hands at 2:00?
Tip: The formula for finding the angle between the hands of a clock at any given time is:
where is the hour, and is the minutes.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Geometry
Clock Angles
Formulas
Hour hand movement: 30 degrees per hour
Minute hand movement: 6 degrees per minute
Angle between hands: |30H - 5.5M|
Theorems
None (Basic clock angle problem)
Suitable Grade Level
Grades 6-8
Related Recommendation
How to Calculate the Angle Between Clock Hands at 5:10
Calculate Clock Hand Angles at 1:35 - Minute and Hour Hand Angles
Clock Angle Problem at 3:25 - Calculate the Angle Between Hour and Minute Hands
Finding Clock Angles and Angle Measurement in Geometry
What is the Angle Between the Hands of a Clock at 8:00?