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Math Help - Somewhat basic Cosine rule problem. Help appreciated

  1. #1
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    Somewhat basic Cosine rule problem. Help appreciated

    First part of the question was easy,

    The second part is where i'm stuck.

    What I have tried :
    -Make d the subject in both cases and have one equal to each other (All that happens is that everything cancels each other out and I get 0=0)
    -Make d^2 the subject (I don't know why I tried this, same result as before >.>)

    Completely lost as to how to solve this problem.
    Any help would be appreciated!
    (Sorry for poor diagram etc. in advance)Somewhat basic Cosine rule problem. Help appreciated-scan_pic0019.jpg

    Click the image to make it larger.
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  2. #2
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    Re: Somewhat basic Cosine rule problem. Help appreciated

    Because alpha +beta=180 then cos(alpha)=-cos(beta), so you can make an equation using results from the first part.
    Thanks from Robert256
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    Re: Somewhat basic Cosine rule problem. Help appreciated

    Quote Originally Posted by biffboy View Post
    Because alpha +beta=180 then cos(alpha)=-cos(beta), so you can make an equation using results from the first part.
    Could you please explain this part to me?
    Thanks for the reply ^_^
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    Re: Somewhat basic Cosine rule problem. Help appreciated

    When 2 angles add up to 180 they have the same numerical value but one is the negative of the other eg cos120 =-cos60, cos110=-cos70 Check some values on your calculator.
    Thanks from Robert256
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    Re: Somewhat basic Cosine rule problem. Help appreciated

    Quote Originally Posted by biffboy View Post
    When 2 angles add up to 180 they have the same numerical value but one is the negative of the other eg cos120 =-cos60, cos110=-cos70 Check some values on your calculator.
    Thanks, I understand completely now.
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  6. #6
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    Re: Somewhat basic Cosine rule problem. Help appreciated

    Quote Originally Posted by biffboy View Post
    When 2 angles add up to 180 they have the same numerical value but one is the negative of the other eg cos120 =-cos60, cos110=-cos70 Check some values on your calculator.
    That's only true for the Cosine and Tangent functions and their reciprocals.

    \cos \(180-\theta)=-\cos \theta

    \sec\(180-\theta)=-\sec\theta

    \tan\(180-\theta)=-\tan\theta

    \cot\(180-\theta)=-\cot\theta

    However,

    \sin(180-\theta)=+\sin \theta

    \csc(180-\theta)=+\csc\theta

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