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Pre-Calculus

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Determine the number of triangles that can be formed with the given information.
and if it forms two possible triangles solve all unknown angles and sides

Angle A=116 degrees
a=10
b=11

  • Pre-Calculus - ,

    One.

    Assuming you are using the standard notoation that
    b is the side opposite angle B etc.

    sinB/11 = sin116°/10
    sin B = .9886
    angle B = appr 81.4° or appr 98.6°
    but the latter is not possible since a triangle cannot have 2 obtuse angles

    so B = 81.4° is the only angle possible,
    thus only one triangle.

    I will leave it up to you to find the other angle and side.

  • Pre-Calculus - ,

    but if you add 81.4 (measure of angle B) plus 116 (measure of angle A) you get 197.368 which is over 180 degrees....
    so that would make measure of angle C negative which is why I'm confused

  • Pre-Calculus - ,

    Of course you are right, silly of me not to even check for the obvious.
    I was too concerned about the two obtuse angles.
    c
    so....
    No such triangle is possible.

  • Pre-Calculus - ,

    thank you so much!!!

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