What are the contents of mathematical photography?

Projective Theorem of Arbitrary Triangle: In triangles A, B and C, it is known that A, B and C are the corresponding sides of triangle inner angles A, B and C respectively, then there are

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 (called height in triangle), so the width is unchanged, and because the area ratio of the plane polygon = the product ratio of the side length. So it is the ratio of the length of the figure (called the height in the triangle).

Extended data

(1) First, the internal angles in the equation are known by sine theorem, and then the size of angle C or the relationship between angles A and B are obtained by sum theorem of internal angles of triangle and sine formula of two angles, so as to judge the shape of triangle ABC.

(2) Combine the cosine theorem with (1) to get a. , and then use the triangle area formula to solve.

Or (1) use the projective theorem of any triangle to replace B and then merge the same types to get the relationship between cosC and edge ab.