Geometry – Solving Triangle Problems with Two Sides and Included Angle

Question

is it possible to find the third side of a triangle if you know the lengths of the other two and the angle between the known sides? the triangle is not equilateral.

we're using the kinect camera and we can find the distance from the camera to the start of a line and the distance to the end of a line, we could calculate the angle between the two lines knowing the maximum vertical and horizontal angle but would it be possible to calculate the length of the line on the ground? the problem is that the camera won't be exactly above the line so the triangle we get wouldn't be equilateral.

Answer 1

How about the law of cosines?

Consider the following triangle $\triangle ABC$, the $ \color{maroon} {\text{poly 1}}$ below, with sides $\color{maroon}{\overline{AB}=c}$ and $\color{maroon}{\overline{AC}=b}$ known. Further the angle between them, $\color{green}\alpha$ is known.

$\hskip{2 in}$

Then, the law of cosines tell you that $$\color{maroon}{a^2=b^2+c^2-2bc\;\cos }\color{blue}{\alpha}$$