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 resulting​ triangle

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Question 1207608: 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 resulting​ triangle(s).
b=8, c=9, B=40degrees

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:


b=8, c=9, B+=40degrees

using law of sine:
b%2Fsin%28B+%29=c%2Fsin%28C+%29
8%2Fsin%2840%29=9%2Fsin%28C%29
sin%28C%29=9sin%2840%29%2F8
sin%28C%29=0.7231360608973567
C=sin%5E-1%280.7231360608973567%29
C=0.8083319666202583
C=46.314
or
C=+133.69°

find third angle

A=180-%2840%2B46.314%29=93.69
or
A=180-%2840%2B133.69%29=6.31

side a=%28b%2Fsin%28B%29%29%2Asin%28A%29
a=%288%2Fsin%2840%29%29%2Asin%2893.69%29
a=12.42
or
a=%288%2Fsin%2840%29%29%2Asin%286.31%29
a=1.37

Solution 1:

Sides:
a+=+12.42
b+=+8
c+=+9
Angles:
A+=+93.69 °
B+=+40 °
C+=+46.314 °

Solution 2:

Sides:
a+=+1.37
b+=+8
c+=+9
Angles:
A+=+6.31 °
B+=+40 °
C+=+133.69+°