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Math Help - The Law of Sines

  1. #1
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    The Law of Sines

    I can easily find the measurements of sides with two angles and one side. What i'm having trouble on is completing and finding all values of a triangle based on one angle and two sides. Here I've drawn up a problem for reference.

    Help
    Attached Thumbnails Attached Thumbnails The Law of Sines-untitled.jpg  
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  2. #2
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    i trust your want to find out what x is,

    you need the sine rule which is
    a/sin A = b/sin B = c/sin C

    we have numbers for c, sin C, b and sin B (its x) so as b/sin B = c/sin C you just rearrange the algebra to get sin B, then it should be easy from their but i will show you anyway

    80.2/sin 67 =56.3/sin x

    80.2sin x = 56.3sin 67

    sin x = 56.3 sin 67/80.2

    x = inverse sin (56.3sin67/80.2)

    x = 40.3 degrees.
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  3. #3
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    Hello, Jonathan!

    It seems to be straight-forward.
    . . Exactly where is your difficulty?

    Code:
                C
                *
               *  *
              * 67 *  a
      b=56.3 *        *
            *           *
           *              *
        A *  *  *  *  *  *  * B
                c=80.2

    From the Law of Sines, we have: . \frac{\sin B}{b} \:=\:\frac{\sin C}{c}\quad\Rightarrow\quad\sin B \:=\:\frac{b\!\cdot\!\sin C}{c}

    Then: . \sin B \:=\:\frac{56.3\sin67^o}{80.2} \:=\:0.646189816

    . . Hence: . \boxed{B \:\approx\:40.25^o}


    Then: . A \;=\;180^o - 67^o - 40.25^o \quad\Rightarrow\quad\boxed{ A\:=\:72.75^o}


    From the Law of Sines, we have: . \frac{a}{\sin A}\:=\:\frac{c}{\sin C}\quad\Rightarrow\quad a \:=\:\frac{c\!\cdot\!\sin A}{\sin C}

    Then: . a \:=\:\frac{80.2\sin72.75^o}{\sin67^o} \:=\:83.18458706

    . . Hence: . \boxed{ a\:\approx\:83.2}

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  4. #4
    Senior Member
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    Hey my difficulty lies in how you got

    40.25 for angle B.

    I know you got .646xxxxx when you found the SIN B figuring it out algebraically. But from this irrational number I don't understand how you got 40.25.

    I experimented and used inverse SIN of .646xxxxx and it gave me 40.25. I still don't understand why we use the inverse. This is my pain and difficulty
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  5. #5
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    we use the inverse sin becasue it reverses sin, thats simply why it cancels cout the effect that sin has on the x leaving us with only x. Its the same i idea as knowing that 7x = 14 we use division to reverse the miultiplication, trig is just the same (not very good at exaplaing maths??? hope it helped if not just ask again)
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