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6.6 The Law of Cosines

Focus on law of cosines and find cosine from sides.

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01Law of Cosines: finding a side (SAS)Worked steps · five questions 02Law of Cosines: finding an angle (SSS)Worked steps · five questions 03Heron's FormulaWorked steps · five questions 04Choosing Law of Sines or Law of CosinesWorked steps · five questions

Lesson brief and rules

6.6 The Law of Cosines

$c^{2}=a^{2}+b^{2}-2ab \cos C$ when $C$ is between sides $a$ and $b$ .

Worked example

1

01 / Two sides of length

4

meet at

60^{\circ}

. Find the square of the opposite side.

02 /

c^{2}=4^{2}+4^{2}-2(4)(4)\cos 60^{\circ}=16

03 / Answer:

16

Worked example 2 · Find cosine from sides

A triangle has sides $4, 4$ , and $4$ . Find the cosine of any angle.

All sides equal, so each angle is $60^{\circ}$ and $\cos 60^{\circ}=\dfrac{1}{2}$ . Answer: $\dfrac{1}{2}$

15 questions covering every idea, with a worked answer for each.Start practice ↗

Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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6.6 The Law of Cosines

Ideas in this lesson

6.6 The Law of Cosines