Math-Geometry

Find the angle that the hr hands and the mins hand made when it at 10:00:45.67

so it 10olock 00 min and 45.67 sec
and find the angles

Show works
it one of those clocks problem

-thanks


We're asked
"Find the angle that the hr hands and the mins hand made when it at 10:00:45.67"

I think one of the first things to do would be to convert the 45.67 to 45 2/3 seconds.
Now lets note that 1min=1/60 of the clockface = (1/60)*360deg=6deg Let's try to make a ballpark estimate too. When it's 10:00 the hands are two hours or 1/6 of the clock face apart, so the angle is 1/6 * 360deg or 60deg. If the minute hand were on the one minute and the hour hand didn't move, then the hands would be exactly 66deg apart. Thus the angle A that we want is 60deg < A < 66deg.
Now how much does the minute hand move in that time? That is, what angle does it make with the 12 during that time?
Well, (45 2/3)sec/60sec * 6deg =
(1) (137/3*60)*6deg=(137/30)deg (this is approx 4.5deg).
Now how much does the hour hand move during that time? We should observe that 1rev of hour hand = 12revs minute hand, thus the hour hand travels 1/12 the distance of the minute hand in the same time period. This means the angle the hour hand makes with the 12 in that time period is
(2) 60deg - (1/12)(137/30)deg = 60deg - 137/360 deg
If we add (1) and (2) we get
60deg - 137/360 deg + (137/30)deg =
60deg + (11*137)/360deg =
(3) 64 67/360 deg
This is very nearly 64.2 deg, but the fraction (3) above is exact.
Unfortunately I see that I haven't left anything for you to do, so try to work another problem from your text, or modify this one slightly to make sure you can do the steps for yourself.


wow nice thanks


You're welcome, but I see I didn't leave any steps for you to do. Try working through a similar problem if it were 10:01:45 or something similar say. Make sure you can work and understand the steps for yourself.

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