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

check

Explanation:

Step1: Identify triangle type

$\triangle CBD$ is a right triangle (right angle at $D$).

Step2: Match to theorem

Right triangles follow the Pythagorean theorem, which states for legs $l_1, l_2$ and hypotenuse $h$: $h^2 = l_1^2 + l_2^2$. Here, hypotenuse is $a$, legs are $(b-x)$ and $h$, so $a^2=(b-x)^2+h^2$.

Answer:

Pythagorean theorem