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Trig

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Should the triangle be solved beginning with Law of Sines of Law of Cosines. Then solve the triangle. Round to the nearest tenth. A=56 degrees, B=38 degrees, a=13.

Sines. I get confused on the formula. I know C=86 degrees

  • Trig - ,

    To solve a triangle you must be given 3 independent bits of information.
    2 sides and 1 angle
    3 sides
    1 side and 2 angles
    (note 3 angles is not "3 independent pieces of information, since if you know 2 angles, you automatically know the third)

    general simple rule:
    If you are given a side and its opposite angle, use the sine law
    if not, use cosine law.

    so for yours, clearly sine law.

  • Trig(I know all of that I just need to know how to use the formula) - ,

    I know I need to use the law of sines but I don't really know how and which one to use like sinA/a= sin B/b and sinB/b =sinC/c and sinA/a = sinC/c. That's where I get confused.

  • Trig - ,

    clearly you are given a side and its opposite angle, a and A, so that is obviously the ratio you are going to use

    SinA/a = SinB/b

    sin56/13 = sin38/b crossmultiply and solve for b.
    b = 13sin38/sin56
    = 9.65

    do the same to find c

  • Trig - ,

    b=9.7(i had to round)

    im not sure if im doing this right.

    SinB/b = SinC/c
    Sin38/9.7 = Sin86/c
    c = 9.7sin38/sin86
    c= 5.98 or 6 since I have to round to nearest tenth.

  • Trig - ,

    why would you not stick with the exact ration sin56/13, which uses the original numbers given

    You used an answer that you obtained after you rounded off that answer, so you are compounding your error.

  • Trig - ,

    so to find c all I have to do is

    Sin56/13 = Sin86/c
    c = 13Sin56/Sin86
    c = 10.8

  • Trig - ,

    NO

    Sin56/13 = Sin86/c now cross-multiply
    csin56 = 13sin86 divide by sin56
    c = 13sin86/sin56
    c = 15.6

    check: in any triangle, your smallest side should be across from the smallest angle, the largest side should be across the largest angle.

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