Find x * y in the following figure. The given figure is not to the scale......?

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  • atsuo
    Lv 6
    2 months ago

    Think △ABC, by the sine law,

    x/sin90° = 2/sin(∠ACB)

    x*sin(∠ACB) = 2*sin90°

    sin(∠ACB) = 2/x

    sinθ = sin(180° - θ), so

    sin(180° - ∠ACB) = 2/x

    sin(∠ACD) = 2/x

    Think △ACD, by the sine law,

    y/sin(∠ACD) = 3/sin30°

    y/(2/x) = 3/(1/2)

    xy/2 = 6

    xy = 12 <--- the answer

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