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Math Help - Stumped with a chords question

  1. #1
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    Stumped with a chords question

    Hey everyone,
    I'm currently working through a basic trigonometry book to re-learn everything I've forgotten since school and I've come to this question: "A circle of radius 45mm has a chord of length 60mm. Find the sine and cosine of the angle at the centre of the circle subtended by this chord." I'd been stuck for quite a while so looked at the answers at the back to see if they would give me a hint as to how to work through it but I could never get to the answers provided which were 0.994 & 0.111. I have actually received a solution from somewhere else on the internet but the answer didn't make any sense to me at all (I have very little intuitive ability when it comes to math) and the source wasn't particularly helpful when asked to explain the solution, but the answer provided was:

    cos(2a)=(sqrt(45^2-30^2)/45)^2-(2/3)^2
    sin(2a)=2(2/3)(sqrt(45^2-30^2)/45)

    I understand that the "45^2-30^2" is Pythag but why divide by 45? Also, the parts that have "2-(2/3)^2" and "2(2/3)" where did these values come from and what are they being used for?

    Very many thanks in advance!
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  2. #2
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    Re: Stumped with a chords question

    Look at this page.
    Go to formula #10 on.
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  3. #3
    Super Member ebaines's Avatar
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    Re: Stumped with a chords question

    I would simply use the law of cosines:

    c^2 = a^2 + b^2 - 2ab cos(c)

    Here a and b both equal 45, and c = 60. Solve for cos(c). Then sin(c) = sqrt(1 - cos^2c)
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