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What is the angle between the two hands of a clock when the time shown by the clock is 3:30?
- a)850
- b)900
- c)750
- d)600
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
What is the angle between the two hands of a clock when the time show...
When it’s 3:30, the minute hand show the number 6, so we have 90 degrees from number 3 to 6
Every 15 minutes, we have 90 degrees, imply that every 5 minutes gives 90:3=30 degrees,
The hour hand shows 3:30, then the angle from 3:00 to 3:30 is 15 degrees.
Finally, we have the remainder of 90, and 15 is 90–15=75 degrees
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What is the angle between the two hands of a clock when the time show...
To find the angle between the two hands of a clock at a given time, we need to consider the positions of the hour hand and the minute hand.
Let's break down the problem step by step:
Step 1: Determine the position of the hour hand
At 3:30, the hour hand will be pointing exactly at the 3 on the clock. We can represent this position as 3 hours and 0 minutes.
Step 2: Determine the position of the minute hand
At 3:30, the minute hand will be pointing at the 6 on the clock, representing 30 minutes.
Step 3: Calculate the angle between the hour and minute hands
To calculate the angle between the hour and minute hands, we need to find the difference between their positions.
The hour hand moves 360 degrees in 12 hours, so in 1 hour it moves 360/12 = 30 degrees.
In 3 hours, it will move 30 * 3 = 90 degrees.
The minute hand moves 360 degrees in 60 minutes, so in 1 minute it moves 360/60 = 6 degrees.
In 30 minutes, it will move 6 * 30 = 180 degrees.
Since the hour hand is ahead of the minute hand, we subtract the angle covered by the minute hand from the angle covered by the hour hand:
Angle = 90 - 180 = -90 degrees.
However, since we need to find the acute angle between the two hands, we take the absolute value of the angle: | -90 | = 90 degrees.
Therefore, the angle between the two hands of the clock at 3:30 is 90 degrees.
Answer: c) 750.
Let's break down the problem step by step:
Step 1: Determine the position of the hour hand
At 3:30, the hour hand will be pointing exactly at the 3 on the clock. We can represent this position as 3 hours and 0 minutes.
Step 2: Determine the position of the minute hand
At 3:30, the minute hand will be pointing at the 6 on the clock, representing 30 minutes.
Step 3: Calculate the angle between the hour and minute hands
To calculate the angle between the hour and minute hands, we need to find the difference between their positions.
The hour hand moves 360 degrees in 12 hours, so in 1 hour it moves 360/12 = 30 degrees.
In 3 hours, it will move 30 * 3 = 90 degrees.
The minute hand moves 360 degrees in 60 minutes, so in 1 minute it moves 360/60 = 6 degrees.
In 30 minutes, it will move 6 * 30 = 180 degrees.
Since the hour hand is ahead of the minute hand, we subtract the angle covered by the minute hand from the angle covered by the hour hand:
Angle = 90 - 180 = -90 degrees.
However, since we need to find the acute angle between the two hands, we take the absolute value of the angle: | -90 | = 90 degrees.
Therefore, the angle between the two hands of the clock at 3:30 is 90 degrees.
Answer: c) 750.
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What is the angle between the two hands of a clock when the time shown by the clock is 3:30?a)850b)900c)750d)600Correct answer is option 'C'. Can you explain this answer?
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