SOLUTION: Two sides and an angle are given below. Determine whether the given information results in one​ triangle, two​ triangles, or no triangle at all. Solve any​ tria

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Question 1075746: Two sides and an angle are given below. Determine whether the given information results in one​ triangle, two​ triangles, or no triangle at all. Solve any​ triangle(s) that results.
b=4,c=5,B=40 degrees
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If you draw AB and angle B,
you realize that there are two possible locations for point C,
at a distance b=4 from A.
There are highlight%282%29 triangles.
Law of sines says that
sin%2840%5Eo%29%2F4=sin%28C%29%2F5 ---> sin%28C%29=about0.80348 ---> system%28red%28C%29=53.464%5Eo%2C%22or%22%2Cgreen%28C%29=126.536%5Eo%29
For the red%28red%29 option,
A=180%5Eo-40%5Eo-53.464%5Eo=86.536%5Eo .
Then, using law of shines again,
a%2Fsin%28A%29=b%2Fsin%28B%29 , with approximate values becomes
a%2F0.998173=4%2F0.642788 ---> a=6.212 .
For the green%28green%29 option,
A=180%5Eo-40%5Eo-126.536%5Eo=13.464%5Eo , and
a=4%2A0.23834%2F0.642788=1.449