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Math Help - computing angle and radius with few infos

  1. #1
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    computing angle and radius with few infos

    hello!
    i have a little question about a trigonometry exercice. and i'm stucked getting the formulas
    is it possible to get the angle and the radius of a circle if i have only the arc length and the chord length of these
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  2. #2
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    Quote Originally Posted by mantus View Post
    hello!
    i have a little question about a trigonometry exercice. and i'm stucked getting the formulas
    is it possible to get the angle and the radius of a circle if i have only the arc length and the chord length of these
    hello , i don think so .

    Let A and B be the arc length and chord length respectively , where their values are known .

    A=r\theta ---1

    B=2r\sin \frac{\theta}{2} ---2

    If you divide the simultaneous equations to solve for \theta

    \frac{A}{B}=\frac{r\theta}{2r\sin \frac{\theta}{2}}

    \frac{A}{B}=\frac{\theta}{2\sin \frac{\theta}{2}}

    For convenience , let \frac{A}{B}=1

    so \theta=2\sin (\frac{\theta}{2}) which i don see how to solve this .
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  3. #3
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    Quote Originally Posted by mantus View Post
    hello!
    i have a little question about a trigonometry exercice. and i'm stucked getting the formulas
    is it possible to get the angle and the radius of a circle if i have only the arc length and the chord length of these
    Yes.

    The circumference of a circle is 2\pi r.

    So the arc length a is \frac{2\pi r \theta}{360} = \frac{\pi r \theta}{180} (if the angle is measured in degrees)

    or

    \frac{2\pi r \theta}{2\pi} = r\theta (if the angle is measured in radians).

    Let's assume that the angle is measured in radians.



    You can also create an isosceles triangle using the chord and 2 radii.

    The angle between them is \theta.

    If we call the chord length l, then by the Cosine Rule we have

    l^2 = r^2 + r^2 + 2r\cdot r \cos{\theta}

    l^2 = 2r^2 + 2r^2\cos{\theta}.


    Now you have two equations in two unknowns.



    Edit: Upon further inspection it doesn't look like these two equations can be solved simultaneously for r and \theta.
    Last edited by Prove It; January 12th 2010 at 05:39 AM.
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