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4.04 The cosine rule

Interactive practice questions

Prove the cosine rule: $a^2=b^2+c^2-2bc\cos A$a2=b2+c22bccosA.

a

Find an expression for $a^2$a2 by using Pythagoras' theorem.

Express your answer in expanded form.

b

Find an expression for $h^2$h2 by using Pythagoras' theorem in $\triangle ACD$ACD.

c

Find an expression for $x$x in terms of $\cos A$cosA.

d

Substitute $h^2=b^2-x^2$h2=b2x2 and $x=b\cos A$x=bcosA into $a^2=h^2+c^2-2cx+x^2$a2=h2+c22cx+x2 to prove the cosine rule.

Medium
7min

Which of the following is true for the given triangle?

Easy
< 1min

To use the cosine rule to find the length of $AC$AC, which angle would need to be given?

Easy
< 1min

Find the length of $a$a using the cosine rule.

Round your answer to two decimal places.

Easy
3min
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Outcomes

1.2.4

establish and use the sine and cosine rules, including consideration of the ambiguous case and the formula Area=1/2 bc sin⁡A for the area of a triangle

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