What is the content of projective theorem in high school mathematics?

Arbitrary triangle projection theorem: In triangle ABC, it is known that a, b, and c are the sides corresponding to the interior angles A, B, and C of the triangle, then we have

a= b cosC+c cosB,

b=c cosA+a cosC,

c=a cosB+b cosA.

Projection is to scale the length of the original figure (height in a triangle), so the width remains unchanged, and because the area ratio of a plane polygon = the product ratio of the side lengths. So it is the ratio of the length of the figure (height in a triangle).

Extended information

(1) First use the sine theorem to reduce the angles in the known equations, and then use the triangle interior angle sum theorem and combine the sine formulas of the two angles to find the angle. The size of C, or the relationship between angles A and B, can determine the shape of triangle ABC.

(2) Use the cosine theorem combined with (1) to obtain a?, and then use the triangle area formula to solve it.

Or (1) use the projection theorem of any triangle to replace b and then merge the same types to get the relationship between cosC and side ab.

Baidu Encyclopedia-Projection Theorem