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    Hi, I need help with a C2 question.

    Triangle ABC is such that BC = 5√2 cm, angle ABC = 30 degrees and angle BAC = θ, where sin θ = √5/8.

    Work out the length of AC, giving your answer in the form a√b, where a and b are integers.

    thank you!
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    Any workings?
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    Sketch it. It's just the sine rule.
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    I can work out an equivalent answer, but I can't keep it in surd form :/
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    Ah, I had this problem last year, if my instincts are correct then use one of the double angle formulae
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    (Original post by BlastOff)
    I can work out an equivalent answer, but I can't keep it in surd form :/
    Well, post your working then.
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    5√2 / √5/8 = x/sin30

    5√2 x sin 30 / √5/8 = 12.6

    The answer to the question is 4√10, which is 12.6
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    5√2 / √5/8 = x/sin30

    But sin30 = 0.5...

    So x/sin30 = x/0.5 = 2x

    So 5√2 / √5/8 = 2x

    Divide through the fraction on the LHS properly and then divide through by 2 to get x as a surd.
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    sine rule...
 
 
 
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