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    Hi all,

    I've been working through this pack,
    https://3f7c9b863b68ba81e37b9436bc95...%20Measure.pdf

    I do not understand how one gets to the answer of the first question (7) part b.
    You can see the question on the above link (the first question) but here it is anyway:

    7. In the triangle ABC, AB = 8 cm, AC = 7 cm, ∠ABC = 0.5 radians and ∠ACB = x radians.

    a) Use the sine rule to find the value of sin x, giving your answer to 3 decimal places.

    This is fine,
    sin(0.5) / 7 = sin(x) / 8
    Therefore sin(x) = (sin(0.5)*8) / 7
    = 0.548 (correct)

    Given that there are two possible values of x,
    (b) find these values of x, giving your answers to 2 decimal places

    ^^^??? How ???^^^
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    Just like where you answer questions in degrees, you have to take into account all other angles that would leave you with the same answer. This is where you would use a CAST diagram, but instead of doing 180-angle, use Pi-angle.
    Therefore,
    pi-(sin(.5)*(8/7))=2.594

    To check you can plug this number into the first equation. You already have the first angle from part A.

    Something to note is that your angle MUST be less than pi-0.5 otherwise all the angles in the triangle are squiffy and there are only 2 angles (same as why there are less than 180degrees in triangle)

    Hope this helps!
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    CAST diagrams or draw the sinx graph. You'll notice two values where your value of sinx intersects the graph y = sinx.
 
 
 
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