Curriculum
Pure Mathematics — Second Secondary
Unit 1: Real Functions and Curve Sketching
0/8
Unit 2: Exponents and Logarithms
0/12
Unit 3: Limits
0/6
Text lesson
The Cosine Rule
The Cosine Rule
Statement of the cosine rule
Statement of the cosine rule
- In any triangle ABC
- let a
- b and c be the lengths of the sides opposite the angles A
- B and C respectively. Then:
a2 = b2 + c2 − 2bc cos A
- Similarly, b2 = a2 + c2 − 2ac cos B, and c2 = a2 + b2 − 2ab cos C.
- The rule can also be written in a form that gives the angle:
cos A = (b2 + c2 − a2) / (2bc)
- The rule is used in two situations:
Key points
Two sides and the included angleto find the third side.
Three sidesto find any angle of the triangle.
Noteif A is a right angle then cos A = 0, and the rule becomes Pythagoras’ theorem, a2 = b2 + c2.
The Cosine Rule · 1 / 5