# How do you solve the triangle using law of sines given a=8, b=9, c=10?

Given three sides of a triangle, angles can be found using cosine rule ans not the Rule of sines. Accordingly,cosA=$\frac{{b}^{2} + {c}^{2} - {a}^{2}}{2 b c}$= $\frac{81 + 100 - 64}{180} = \frac{17}{180.} A = a r c \cos \left(\frac{117}{180}\right)$ = 49.45degrees. Like wise cosB= $\frac{83}{160}$. B= arc cos(83/160)=58.75 degrees. Then finally C= 180-49.45-58.75= 71.20