SOLUTION: In a triangle ABC we have angle A=62 degrees, side a=6, side b=10. Find the length of c.

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Question 1197886: In a triangle ABC we have angle A=62 degrees, side a=6, side b=10. Find the length of c.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Try drawing the figure. Law Of Sines to help first get measure of the angle at B.
sin%28B%29%2F10=sin%2862%29%2F6

Find angle measure at c, from this; and then your choice Law Of Cosines or Law Of Sines to find c.

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

            This task is a trap to catch inattentive readers in it.
            Such a triangle,  as described in the post,  does not exist.


Indeed,  had it exist,  we could write the sine law

        sin%28A%29%2Fa = sin%28B%29%2Fb
  or
        sin%2862%5Eo%29%2F6 = sin%28B%29%2F10.

From this proportion,   sin(B) = %2810%2F6%29%2Asin%2862%5Eo%29 = %2810%2F6%29%2A0.88294759285 = 1.471579321.

Since this value is greater than  1,  it creates a  CONTRADICTORY.


ANSWER.   Such a triangle as described in the post  DOES  NOT  EXIST.


                        Solved.


Such a triangle  DOES  NOT  EXIST.

        Such a triangle  DOES  NOT  EXIST.

                Such a triangle  DOES  NOT  EXIST.