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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!

Attachment image

2 Answers

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  • 2 months ago
    Favorite 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

    :)>

  • 2 months ago

    I don't see any attached picture.

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