Calculate Angles from the Three Sides of a Triangle

The answer is given in degrees, minutes, and seconds (° ′ ″ ), rounded to 2 decimal places for the seconds.

\(\normalsize Triangle\hspace{20px} using\ Heron's\ formula\\ (1)\ S=\sqrt{s(s-a)(s-b)(s-c)},\hspace{10px} s={\large \frac{(a+b+c)}{2}}\\ (2)\ if\ a\ge b,c\hspace{20px} h={\large\frac{2S}{a}},\ B=\sin^{\tiny -1}{\large\frac{h}{c}},\ C=\sin^{\tiny -1}{\large\frac{h}{b}}\\ \hspace{25px}if\ b\ge c,a\hspace{20px} h={\large\frac{2S}{b}},\ C=\sin^{\tiny -1}{\large\frac{h}{a}},\ A=\sin^{\tiny -1}{\large\frac{h}{c}}\\ \hspace{25px}if\ c\ge a,b\hspace{20px} h={\large\frac{2S}{c}},\ A=\sin^{\tiny -1}{\large\frac{h}{b}},\ B=\sin^{\tiny -1}{\large\frac{h}{a}}\\ (3)\ A+B+C=180\\\)