Given: with altitude h.

Two right triangles are formed: one with side lengths , h, and b, and one with side lengths r, h, and a.

A diagram of the triangle ABC. A dashed perpendicular line is drawn outside the triangle from the top vertex C to the base. This line joins B. The length of AB is c, AC is b, BC is a the height of the perpendicular line is h and the base is r.

Carson starts the proof of the law of cosines with by the definition of the sine ratio and by the definition of the cosine ratio.

What are the next steps in the proof?

Use the

to rewrite each trigonometric equation in terms of the numerator.

Then, Carson can write an expression for side
in terms of
.

Next, he can use the
to relate a, b, c, and A.