Solve {l}{cos(A)=3/5}{cos(B)=5/13}{A+B+C=pi}{b=3}{a=C}{text{Solvefor}ctext{where}}{c=a}

$$\left. \begin{array} { l } { \cos(A) = \frac{3}{5} }\\ { \cos(B) = \frac{5}{13} }\\ { A + B + C = \pi }\\ { b = 3 }\\ { a = C }\\ { \text{Solve for } c \text{ where} } \\ { c = a } \end{array} \right.$$

Solve for A, B, C, b, a, c

$$A=2\pi n_{1}+\arccos(\frac{3}{5})\text{, }n_{1}\in \mathrm{Z}\text{, }B=2\pi n_{3}+\arccos(\frac{5}{13})\text{, }n_{3}\in \mathrm{Z}\text{, }C\in \cup n_{1},2\pi n_{1}-2\pi n_{3}+\pi -\arccos(\frac{5}{13})-\arccos(\frac{3}{5})\text{, }n_{3}\in \mathrm{Z}\text{, }b=3\text{, }a\in \cup n_{3},\cup n_{1},\cup n_{3},\cup n_{1},2\pi n_{1}-2\pi n_{3}+\pi -\arccos(\frac{5}{13})-\arccos(\frac{3}{5})\text{, }C=2\pi n_{1}-2\pi n_{3}+\pi -\arccos(\frac{5}{13})-\arccos(\frac{3}{5})\text{, }n_{3}\in \mathrm{Z}\text{, }c\in \cup n_{3},\cup n_{3},\cup n_{1},\cup n_{3},\cup n_{3},\cup n_{1},\cup n_{3},\cup n_{1},2\pi n_{1}-2\pi n_{3}+\pi -\arccos(\frac{5}{13})-\arccos(\frac{3}{5})\text{, }a=2\pi n_{1}-2\pi n_{3}+\pi -\arccos(\frac{5}{13})-\arccos(\frac{3}{5})\text{ and }C=2\pi n_{1}-2\pi n_{3}+\pi -\arccos(\frac{5}{13})-\arccos(\frac{3}{5})\text{, }\exists n_{3}\in \mathrm{Z}\text{ : }\left(\exists n_{1}\in \mathrm{Z}\text{ : }C=2\pi n_{1}-2\pi n_{3}+\pi -\arccos(\frac{5}{13})-\arccos(\frac{3}{5})\right)\text{, }n_{3}\in \mathrm{Z}$$

$$A=2\pi n_{1}+\arccos(\frac{3}{5})\text{, }n_{1}\in \mathrm{Z}\text{, }B=2\pi n_{6}+2\pi -\arccos(\frac{5}{13})\text{, }n_{6}\in \mathrm{Z}\text{, }C\in \cup n_{1},2\pi n_{1}-2\pi n_{4}-\left(\pi +\arccos(\frac{3}{5})-\arccos(\frac{5}{13})\right)\text{, }n_{4}\in \mathrm{Z}\text{, }b=3\text{, }a\in \cup n_{4},\cup n_{1},\cup n_{4},\cup n_{1},2\pi n_{1}-2\pi n_{4}-\left(\pi +\arccos(\frac{3}{5})-\arccos(\frac{5}{13})\right)\text{, }C=2\pi n_{1}-2\pi n_{4}-\left(\pi +\arccos(\frac{3}{5})-\arccos(\frac{5}{13})\right)\text{, }n_{4}\in \mathrm{Z}\text{, }c\in \cup n_{4},\cup n_{4},\cup n_{1},\cup n_{4},\cup n_{4},\cup n_{1},\cup n_{4},\cup n_{1},2\pi n_{1}-2\pi n_{4}-\left(\pi +\arccos(\frac{3}{5})-\arccos(\frac{5}{13})\right)\text{, }a=2\pi n_{1}-2\pi n_{4}-\left(\pi +\arccos(\frac{3}{5})-\arccos(\frac{5}{13})\right)\text{ and }C=2\pi n_{1}-2\pi n_{4}-\left(\pi +\arccos(\frac{3}{5})-\arccos(\frac{5}{13})\right)\text{, }\exists n_{4}\in \mathrm{Z}\text{ : }\left(\exists n_{1}\in \mathrm{Z}\text{ : }C=2\pi n_{1}-2\pi n_{4}-\left(\pi +\arccos(\frac{3}{5})-\arccos(\frac{5}{13})\right)\right)\text{, }n_{4}\in \mathrm{Z}$$

$$A=2\pi n_{5}+2\pi -\arccos(\frac{3}{5})\text{, }n_{5}\in \mathrm{Z}\text{, }B=2\pi n_{3}+\arccos(\frac{5}{13})\text{, }n_{3}\in \mathrm{Z}\text{, }C\in \cup n_{2},2\pi n_{2}-2\pi n_{3}-\left(\pi +\arccos(\frac{5}{13})-\arccos(\frac{3}{5})\right)\text{, }n_{3}\in \mathrm{Z}\text{, }b=3\text{, }a\in \cup n_{3},\cup n_{2},\cup n_{3},\cup n_{2},2\pi n_{2}-2\pi n_{3}-\left(\pi +\arccos(\frac{5}{13})-\arccos(\frac{3}{5})\right)\text{, }C=2\pi n_{2}-2\pi n_{3}-\left(\pi +\arccos(\frac{5}{13})-\arccos(\frac{3}{5})\right)\text{, }n_{3}\in \mathrm{Z}\text{, }c\in \cup n_{3},\cup n_{3},\cup n_{2},\cup n_{3},\cup n_{3},\cup n_{2},\cup n_{3},\cup n_{2},2\pi n_{2}-2\pi n_{3}-\left(\pi +\arccos(\frac{5}{13})-\arccos(\frac{3}{5})\right)\text{, }a=2\pi n_{2}-2\pi n_{3}-\left(\pi +\arccos(\frac{5}{13})-\arccos(\frac{3}{5})\right)\text{ and }C=2\pi n_{2}-2\pi n_{3}-\left(\pi +\arccos(\frac{5}{13})-\arccos(\frac{3}{5})\right)\text{, }\exists n_{3}\in \mathrm{Z}\text{ : }\left(\exists n_{2}\in \mathrm{Z}\text{ : }C=2\pi n_{2}-2\pi n_{3}-\left(\pi +\arccos(\frac{5}{13})-\arccos(\frac{3}{5})\right)\right)\text{, }n_{3}\in \mathrm{Z}$$

$$A=2\pi n_{5}+2\pi -\arccos(\frac{3}{5})\text{, }n_{5}\in \mathrm{Z}\text{, }B=2\pi n_{6}+2\pi -\arccos(\frac{5}{13})\text{, }n_{6}\in \mathrm{Z}\text{, }C\in \cup n_{2},2\pi n_{2}-2\pi n_{4}+\arccos(\frac{5}{13})+\arccos(\frac{3}{5})-3\pi \text{, }n_{4}\in \mathrm{Z}\text{, }b=3\text{, }a\in \cup n_{4},\cup n_{2},\cup n_{4},\cup n_{2},2\pi n_{2}-2\pi n_{4}+\arccos(\frac{5}{13})+\arccos(\frac{3}{5})-3\pi \text{, }C=2\pi n_{2}-2\pi n_{4}+\arccos(\frac{5}{13})+\arccos(\frac{3}{5})-3\pi \text{, }n_{4}\in \mathrm{Z}\text{, }c\in \cup n_{4},\cup n_{4},\cup n_{2},\cup n_{4},\cup n_{4},\cup n_{2},\cup n_{4},\cup n_{2},2\pi n_{2}-2\pi n_{4}+\arccos(\frac{5}{13})+\arccos(\frac{3}{5})-3\pi \text{, }a=2\pi n_{2}-2\pi n_{4}+\arccos(\frac{5}{13})+\arccos(\frac{3}{5})-3\pi \text{ and }C=2\pi n_{2}-2\pi n_{4}+\arccos(\frac{5}{13})+\arccos(\frac{3}{5})-3\pi \text{, }\exists n_{4}\in \mathrm{Z}\text{ : }\left(\exists n_{2}\in \mathrm{Z}\text{ : }C=2\pi n_{2}-2\pi n_{4}+\arccos(\frac{5}{13})+\arccos(\frac{3}{5})-3\pi \right)\text{, }n_{4}\in \mathrm{Z}$$