Scalene Triangle
Calculates the values of the other elements of a scalene triangle based on three selected input values.
| \(\normalsize Scalene\ triangle\\ (1)\ height:\hspace{10px}h=b\cdot \sin C=c\cdot \sin B\\ (2)\ angle:\hspace{12px}B=\sin^{\small-1}{\large\frac{h}{c}}\ ,\hspace{20px}C = \sin^{\small-1}{\large\frac{h}{b}}\\ (3)\ side:\hspace{25px} c=\sqrt{a^2+b^2-2ab\cdot \cos C}\\ (4)\ area:\hspace{25px}S={\large\frac{1}{2}}ah={\large\frac{1}{2}}ab\cdot \sin C\\ \hspace{100px}={\large\frac{1}{2}}a^2{\large\frac{\sin B \sin C}{\sin(B+C)}}\\ \hspace{100px}=\sqrt{s(s-a)(s-b)(s-c)}\\ \hspace{200px}s={\large\frac{a+b+c}{2}}\\ \) |
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