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

Which Of The Following Could Be The First Step To Prove The Law Of Cosines Using The Triangle Below class=

Sagot :

Answer: Option C

[tex]a^2=h^2+(b-r)^2[/tex]

Explanation:

In the triangle below:

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

[tex]\begin{gathered} AC=AD+DC \\ b=r+DC \\ \implies DC=b-r \end{gathered}[/tex]

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

[tex]a^2=h^2+(b-r)^2[/tex]

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

View image ChesneeK176252
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