`A = 58^@, a = 11.4, b = 12.8` Use the law of sines to solve (if possible) the triangle. If two solutions exist, find both. Round your...

Given: `A=58^@, a=11.4, b=12.8`

Law of Sines  `a/sin(A)=b/sin(B)=c/sin(C)`

Triangle #1

`11.4/sin(58)=12.8/sin(B)=c/sin(C)`

`11.4/sin(58)=12.8/sin(B)`

`sin(B)=[12.8sin(58)]/11.4`

`sin(B)=.9522`

`B=arcsin(.9522)`

`B=72.21^@`

`C=180-58-72.21`

`C=49.79^@`

`11.4/sin(58)=c/sin(49.79)`

`c=[11.4sin(49.79)]/sin(58)`

`c=10.27`

Triangle #2

`B=180-72.20`

`B=107.80^@`

`C=180-58-107.80`

`C=14.20^@`

`11.4/sin(58)=c/sin(14.20)`

`c=[11.4sin(14.20)]/sin(58)`

`c=3.30`