Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. **There will be no changes to other Yahoo properties or services, or your Yahoo account.** You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

# AS maths trig question?

Yahya is attempting to prove the cosine rule for the triangle shown below. He starts by adding the dotted lines as shown (see attached picture)

Here are the first few lines of his proof:

Y^2 = c^2 - (b+x)^2 ( Pythagoras)

Y^2 = a^2 - x^2 (Pythagoras)

C^2 - b^2 -2bx = a^2 ( equating expressions and tidying up)

Complete his proof explaining clearly what you have done.

I really have no idea what to do next and I can’t find any similar proofs online so some help would really be much appreciated. Thanks!

### 2 Answers

- Wayne DeguManLv 72 months agoFavorite Answer
c² - b² - 2bx = a²

so, c² = a² + b² + 2bx

From the diagram, x = acos(180 - C)

Now, cos(180 - C) = -cosC

so, x = -acosC

Hence, c² = a² + b² + 2b(-acosC)

i.e. c² = a² + b² - 2abcosC

:)>