Area of a Triangle (From One Side and Two Angles)
Calculate the area, perimeter, and height of a triangle given one side and the two adjacent angles.
| Area S | |
| Perimeter L | |
| Height h |
| \(\normalsize Triangle\ (a,\theta_1,\theta_2\rightarrow S)\\ (1)\ area:\hspace{50px} S={\large\frac{a^2}{2}}{\large\frac{\sin{\theta_1}\sin{\theta_2}}{\sin{(\theta_1+\theta_2)}}}\\ (2)\ height:\hspace{40px} h=a{\large\frac{\tan\theta_1\tan\theta_2}{\tan\theta_1+\tan\theta_2}}\\ (3)\ perimeter:\ L=a \left ( 1 + {\large\frac{\sin\theta_2}{\sin(\theta_1+\theta_2)}}+{\large\frac{\sin\theta_1}{\sin(\theta_1+\theta_2)}} \right ) \\ \) |
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