The Law of Cosine can be used to solve triangles in 2 circumstances: - Given all 3 sides (SSS) - Given 2 sides and the included angle (SAS)
Given this triangle: [ Insert Screenshot image of triangle ]
With the triangle above, the coordinates of B are the hardest to find. We can find it with the formulas:
cos(A) = x/c = ©cos(A) = x;
sin(A) = h/c = ©sin(A) = h;
Those both would be plotted as: (©cos(A), ©sin(A)).
We also will need the distance formula for finding the distance between points (x1, y1) and (x2, y2).
“cos(A) = x/c = ©cos(A) = x;
sin(A) = h/c = ©sin(A) = h;
Those both would be plotted as: (©cos(A), ©sin(A))”
Distance Formula: d = sqrt((x2-x1)2 + (y2-y1)2)
This would be converted into The Law of Cosine through:
[ Insert image of proof of Law of Cosine screenshot ]
Laws of Cosine: - a2 = b2 + c2 - 2 * b * c * cos(A) - b2 = a2 + c2 - 2 * a * c * cos(B) - c2 = a2 + b2 - 2 * a * b * cos©