Follow these steps to derive the law of cosines
1. The relationship between the side lengths in triangle ABD is
c^2 = x^2 + h^2 by the ans: Pythagorean theorem
2. The relationship between the side lengths in triangle CBD is
a^2 = (b - x)^2 + h^2 by the ans: Pythagorean theorem
3. The equation a^2 = (b-x)^2 + h^2 is ans: expanded to become
a^2 = b^2 - 2bx + x^2 + h^2
4. Using the equation from step 1, the equation
a^2 = b^2 - 2bx + x^2 + h^2 becomes a^2 = b^2 - 2bx + c^2
by ans: substitution
5. in triangle ABD, the trigonometric function ans: cos(A) = x/c
6. Multiply both sides of the equation in step 5 by ans: c
to get x = c cos(A)
7. Substitute ans: c cos(A) for the variable x in the equation
a^2 = b^2 - 2bx + c^2 to produce a^2 = b^2 - 2bc cos(A) + c^2.
8. The law of cosines is obtained by ans: rearranging the previous equation

I got this right I am posing for others feel free to take the points.