Thread: Time: What is the 1st time after 4:30 that min&hr hands don't form acute angle

1. Time: What is the 1st time after 4:30 that min&hr hands don't form acute angle

How would you solve this?

Note: it is on a circular alarm clock

How would you mathematically solve this? I have tried drawing it out, but I do not understand the steps. Thanks!

Choices are as follows:

- 4:35
- 4:36
- 4:37
- 4:38
- 4:39

Thanks!

2. Re: Time: What is the 1st time after 4:30 that min&hr hands don't form acute angle

clockwise from 12, each number on the clock-face is spaced apart 1/12 of a revolution = 30 degrees

at 4:30, the hour hand is halfway between 4 and 5 = 135 degrees from 12, and moves 30 degrees/hr = 1/2 degree/min

at 4:30, the minute hand is at 6 = 180 degrees from 12, and moves 360 degrees/hr = 6 degrees/min

at 4:30, the angle between the hour and minute hand is 180-135 = 45 degrees and the angle between them is increasing at a rate of 6 - (1/2) = 5.5 degrees/min

can you figure the first time the angle between the hands will be > 90 degrees?

3. Re: Time: What is the 1st time after 4:30 that min&hr hands don't form acute angle

"clockwise from 12, each number on the clock-face is spaced apart 1/12 of a revolution = 30 degrees"
yep, im with you...360 degrees in circle...divide by 12 since there are twelve big tick marks

"at 4:30, the hour hand is halfway between 4 and 5 = 135 degrees from 12, and moves 30 degrees/hr = 1/2 degree/min"
i agree with the halfway part, but wouldn't it be around 132.5 degrees?

"at 4:30, the minute hand is at 6 = 180 degrees from 12, and moves 360 degrees/hr = 6 degrees/min"
agreed

"at 4:30, the angle between the hour and minute hand is 180-135 = 45 degrees and the angle between them is increasing at a rate of 6 - (1/2) = 5.5 degrees/min"
again, are u sure it is 135? (not to sound rude or anything)

"can you figure the first time the angle between the hands will be > 90 degrees?"
thats why im here
hm..first time the hands will be less than 90? do u mean greater than 90?

acute is less than 90 degrees?

4. Re: Time: What is the 1st time after 4:30 that min&hr hands don't form acute angle

Originally Posted by Frustration
"clockwise from 12, each number on the clock-face is spaced apart 1/12 of a revolution = 30 degrees"
yep, im with you...360 degrees in circle...divide by 12 since there are twelve big tick marks

"at 4:30, the hour hand is halfway between 4 and 5 = 135 degrees from 12, and moves 30 degrees/hr = 1/2 degree/min"
i agree with the halfway part, but wouldn't it be around 132.5 degrees?

what is half of 30 degrees?

"at 4:30, the minute hand is at 6 = 180 degrees from 12, and moves 360 degrees/hr = 6 degrees/min"
agreed

"at 4:30, the angle between the hour and minute hand is 180-135 = 45 degrees and the angle between them is increasing at a rate of 6 - (1/2) = 5.5 degrees/min"
again, are u sure it is 135? (not to sound rude or anything)

I'm sure ... what about you?

"can you figure the first time the angle between the hands will be > 90 degrees?"
thats why im here
hm..first time the hands will be less than 90? do u mean greater than 90?

I mean greater than or equal to 90 ... review the definition of an acute angle.

acute is less than 90 degrees?
Re: Time: What is the 1st time after 4:30 that min&hr hands don't form acute angle
read the question you posted again ...

6. Re: Time: What is the 1st time after 4:30 that min&hr hands don't form acute angle

Half of 30 degrees is 15, but I don't understand how that pertains to the problem ;/
There are 60 tick marks in a circular clock and 360 degrees in a circle. 360/60 = 6
6 degrees between each tick

the hour hand is between the 4 and the 5; therefore, wouldn't it be around 133?
----
""can you figure the first time the angle between the hands will be > 90 degrees?"
thats why im here
hm..first time the hands will be less than 90? do u mean greater than 90?

I mean greater than or equal to 90 ... review the definition of an acute angle.

acute is less than 90 degrees?"

ohh, i read it wrong; i thought u posted < 90
well even with all the hints u provided, i cannot find the solution
ive tried not doing it mathematically and doing it in my head but...didn't work
ive tried turning the clock so that it is greater than 90 but no it has been a failure

7. Re: Time: What is the 1st time after 4:30 that min&hr hands don't form acute angle

the hour hand is between the 4 and the 5; therefore, wouldn't it be around 133?
No. Look at the picture of the clock again.

There are 30 degrees between each number on the clock face ... the hour hand is halfway between the numbers 4 and 5 ... relative to the position of the number 12, 4(30) + 15 = 135 degrees.

Note that you are dealing with the angular position of each moving hand relative to 12. I've given you their respective angular positions relative to 12 starting at 4:30, the difference between their relative positions at 4:30, and the rate they move relative to each other ...

angle between them = $45^\circ + (5.5 \, \text{deg/min})(t \, \text{min})$

you want to determine when the angle between them is greater than or equal to 90 degrees

8. Re: Time: What is the 1st time after 4:30 that min&hr hands don't form acute angle

Originally Posted by skeeter
No. Look at the picture of the clock again.

There are 30 degrees between each number on the clock face ... the hour hand is halfway between the numbers 4 and 5 ... relative to the position of the number 12, 4(30) + 15 = 135 degrees.
Oh, ok. I get the 135 degrees now. Thank you
Note that you are dealing with the angular position of each moving hand relative to 12. I've given you their respective angular positions relative to 12 starting at 4:30, the difference between their relative positions at 4:30, and the rate they move relative to each other ...

angle between them = $45^\circ + (5.5 \, \text{deg/min})(t \, \text{min})$

you want to determine when the angle between them is greater than or equal to 90 degrees
Ok, so I'm getting the feeling that it's around 4:37? That's in the middle of the the number hands 7 and 8. What am I doing wrong
4:37 is when it is a right angle? Or is it 4:38?

9. Re: Time: What is the 1st time after 4:30 that min&hr hands don't form acute angle

at 4:39 ...

45 + 5.5(9) = 94.5 > 90

at 4:38 ...

45 + 5.5(8) = 89 < 90

10. Re: Time: What is the 1st time after 4:30 that min&hr hands don't form acute angle

Originally Posted by Frustration
Ok, so I'm getting the feeling....
Maths is not about getting "feelings"....get it?

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angle of 4:30 am

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