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Question 827842: the clock reads 8:09, what is the exact measure of the angle formed by the hour and minute hands? Assume that each hands move continuously at a constant rate. Thus, in any given fractional part of an hour, each hand will move that same fractional part of an hour's worth of movement.
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! Your objectives are find where the minute hand points and where the hour hand points.
Using 0 degrees for the "12" position, the minute hand showing "9" is moved (9/60)*360 degrees from the "12".
This is 54 degrees from the "12".
The count of 8 hour is a little different. We focus on how far the hand has rotated from the 8 to the 9 marks. This is (9/60)(360) of the way from 8 to 9 on the clock face. "8" is (8/12)*360 degrees and "9" is (9/12)*360 degrees.
That is (2/3)360 and (3/4)360;
which is 240 and 270 degrees from "12". This is a difference of 30 degrees.
What is 9/60 of 30 degrees? It is (9/60)(30)=4.5 degree.
The hour hand points to 240+4.5 degrees from the "12".
The hour hand points to 244.5 degrees from the "12".
NEARLY DONE: Now you put these together.
Minute hand 54 degrees from the "12", and hour hand 244.5 degrees from the "12"
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