Question

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 pythagorean theorem.
✓ 2. the relationship between the side lengths in $\triangle cbd$ is
$a^{2}=(b - x)^{2}+h^{2}$ by the pythagorean theorem.
✓ 3. the equation $a^{2}=(b - x)^{2}+h^{2}$ is expanded to become
$a^{2}=b^{2}-2bx+x^{2}+h^{2}$.

1. 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

Explanation:

Step1: Identify substitution source

From step 1, $c^2 = x^2 + h^2$

Step2: Substitute into expanded equation

Replace $x^2 + h^2$ in $a^2 = b^2 - 2bx + x^2 + h^2$ with $c^2$

Answer:

substituting $c^2 = x^2 + h^2$ (substitution)