What is the content of the Projection Theorem?

Right-angled triangle projection theorem

In a right-angled triangle, the height on the hypotenuse is the middle term of the ratio of the projections of the two right-angled sides on the hypotenuse. Each right-angled side is this right-angled side The projection on the hypotenuse and the median term of the ratio of the hypotenuse.

The Projection Theorem of Any Triangle

The Projection Theorem of Any Triangle is also known as the "First Cosine Theorem": Suppose △ABC The three sides are a, b, and c, and the angles they subtend are A, B, and C respectively, then a=b·cosC＋c·cosB, b=c·cosA+a·cosC, c=a·cosB+b·cosA. Note: Taking "a=b·cosC＋c·cosB" as an example, the projections of b and c on a are b·cosC and c·cosB respectively, hence the name Projection Theorem. Proof 1: Let the projection of point A on straight line BC be a point D, then the projections of AB and AC on the straight line BC are BD and CD respectively, and BD=c·cosB, CD=b·cosC, ∴a=BD+CD=b·cosC＋c·cosB. The rest can be proved in the same way.