Interactive practice questions
Prove the cosine rule: $a^2=b^2+c^2-2bc\cos A$a2=b2+c2−2bccosA.
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=b2−x2 and $x=b\cos A$x=bcosA into $a^2=h^2+c^2-2cx+x^2$a2=h2+c2−2cx+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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