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Math Help - The measure of an angle.

  1. #1
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    The measure of an angle.

    Ok, this has probably already been asked and solved; if so, please link me. Spent hours upon hours looking this up and I can't get anywhere.

    In short, think of a clock; the hour hand is always at 12 and the second hand rotates around like normal.

    What I know:
    The radius of the circle and the length of the lines.

    I need to know the formula for the angle measure where the hour hand and the second hand intersect?

    Thanks in advance
    A programmer who's eyes hurt.
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  2. #2
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    Quote Originally Posted by NJDubois View Post
    ...

    In short, think of a clock; the hour hand is always at 12 and the second hand rotates around like normal.
    ...
    I need to know the formula for the angle measure where the hour hand and the second hand intersect?

    ....
    Both hands point at the 12. Consider a period of 12 h. During this time the hour hand and the second hand (btw that's really a nice expression ) will meet

    (12 \cdot 60 - 1) times = 719 times

    That means after \frac1{719} \cdot 12\ hours the hand meat again. Since 1 hour is related to 30 with the hour hand the angle is:

    \frac1{719} \cdot 12 \cdot 30^\circ = \frac{360}{719}^\circ~\approx~ 0.50069541^\circ

    That's the angle the hour hand describes between two intersections.
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