Results 1 to 10 of 10

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

  1. #1
    Junior Member
    Joined
    Feb 2015
    From
    Earth
    Posts
    29
    Thanks
    6

    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!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,107
    Thanks
    3647

    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?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2015
    From
    Earth
    Posts
    29
    Thanks
    6

    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?
    Last edited by Frustration; Apr 3rd 2015 at 11:48 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,107
    Thanks
    3647

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

    Quote Originally Posted by Frustration View Post
    "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 ...
    Attached Thumbnails Attached Thumbnails Time: What is the 1st time after 4:30 that min&hr hands don't form acute angle-clock-face-hours.png  
    Last edited by skeeter; Apr 3rd 2015 at 12:12 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    1,671
    Thanks
    313

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

    ClockShop Ad: If your clock don't tick, tock to us !
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Feb 2015
    From
    Earth
    Posts
    29
    Thanks
    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
    my bad
    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
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,107
    Thanks
    3647

    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
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Feb 2015
    From
    Earth
    Posts
    29
    Thanks
    6

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

    Quote Originally Posted by skeeter View Post
    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?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,107
    Thanks
    3647

    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
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    1,671
    Thanks
    313

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

    Quote Originally Posted by Frustration View Post
    Ok, so I'm getting the feeling....
    Maths is not about getting "feelings"....get it?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Oct 26th 2014, 10:24 AM
  2. Replies: 5
    Last Post: May 23rd 2014, 10:04 AM
  3. Replies: 1
    Last Post: Dec 9th 2012, 02:46 AM
  4. Replies: 3
    Last Post: Dec 6th 2010, 02:52 AM
  5. angles between clock hands of the Time = 11:08
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: Nov 29th 2010, 12:25 PM

Search tags for this page

Search Tags


/mathhelpforum @mathhelpforum