Positioning a Mouse with Trigonometry

I've been trying to figure out what logic I need to determine the pose of my robot entirely from its distance sensors. Using the power of CAD, I was able to figure out what variables I knew and what I needed to solve for. Because the beams always shot out from the same place, I always know where they intersect. Fusion360 tells me that the forward-facing beam travels 25.00 mm before intersecting with the 45° beam that traveled 24.04 mm.

I've labeled the sides a, b, and c. Then the angles are α, β, and γ.

I can find c from knowing a, b and γ: c = \sqrt{a^2 + b^2 − 2ab \cos⁡(γ)} I optimized this from knowing that \gamma is always 45° so \cos(γ) will always be \frac{\sqrt{2}}{2}. Therefore, I can simplify - 2ab\cos(\gamma) with a compile-time constant into -ab*core::f32::SQRT_2. This should definitely save several CPU cycles.

c can then be substituted into this equation to get \alpha: α = \cos^{-1}(\frac{b^2+c^2−a^2}{2bc}) Then, if I wanted β, the angles add up to 180: β + α + γ = 180°

BTW: my actual script does everything in radians, but it is definitely easier to visualize things with angles in degrees.

Next steps: create logic for mapping straightaways and diagonals. Maybe even creating a serial program to watch the map it creates.