Question

Which of the following could be the first step to prove the Law of Cosines using the triangle below?

Answer 1

Answer: Option C

`a^2=h^2+(b-r)^2`

Explanation:

In the triangle below:

If AC=b and AD=r, by the segment addition postulate:

`\begin{gathered} AC=AD+DC \\ b=r+DC \\ \implies DC=b-r \end{gathered}`

Therefore, applying the Pythagorean theorem to the right triangle BDC:

`a^2=h^2+(b-r)^2`

The first step to proving the Law of Cosines is Option C.