# Area of a triangle given base and angles

## Calculates the area, perimeter and height of a triangle given the base and two angles.

angle θ1
angle θ2
 same unit as θ1
base a

area S
perimeter L
height h

 $\normal Triangle\ (a,b,\theta\rightarrow S)\\(1)\ area:\hspace{50} S={\large\frac{a^2}{2}}{\large\frac{\sin{\theta_1}\sin{\theta_2}}{\sin{(\theta_1+\theta_2)}}}\\(2)\ height:\hspace{40} h=a{\large\frac{\tan\theta_1\tan\theta_2}{\tan\theta_1+\tan\theta_2}}\\(3)\ perimeter:\ L=a+{\large\frac{h}{\sin\theta_1}}+{\large\frac{h}{\sin\theta_2}}\\$

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