I have one Area of Triangle, One adjacent angle, and one side. Is it possible to calculate all other sides and angles ?
I have searched this problem, but could not get any reference to it.
trianglestrigonometry
I have one Area of Triangle, One adjacent angle, and one side. Is it possible to calculate all other sides and angles ?
I have searched this problem, but could not get any reference to it.
Best Answer
Note that if $a$ and $b$ are two sides of the triangle and $\gamma$ is the angle in between then its Area is $$\text{Area}=\frac{a\cdot b\cdot\sin(\gamma)}{2}\implies b=\frac{2\cdot \text{Area}}{a\cdot \sin(\gamma)}$$ and we find another side. For the third side use the Heron's formula or the Law of Cosines and finally find the remaining angles from the Law of Sines. Can you take it from here?