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