Find a side of a triangle by the cosine formula

Follow this one with me, a step at a time. Try to guess each step first.

Worked example 1

In △ABC, AC = 7 cm, BC = 10 cm and ∠C = 120°. Find AB in cm, in surd form.

Remember: You know two sides and the angle between them, so use the cosine formula: a² = b² + c² − 2bc cos A.

AB² = 7² + 10² − 2(7)(10) cos 120°, and cos 120° = −1/2.
AB² = 49 + 100 + 70, which is 219.
So AB = √219 cm.

Common mistakes

Used the wrong sign for the last term. Check the sign of cos C.
Stopped at the square of the side. Take the square root.
Used Pythagoras’ theorem, which needs a right angle.