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Overview
Advanced Mathematics 2200
Trigonometry
3. NL.SO.2200T3
3.2 Law of cosines
Law of Cosines
The rule that relates the three sides of any triangle to one of its angles, for solving oblique triangles.
What You'll Learn
The law of cosines relates the three sides of any triangle to one of its angles.
The formula is c² = a² + b² - 2ab cos(C).
Use it for SAS (find the third side) or SSS (find an angle).
At 90 degrees the cosine term vanishes and it becomes the Pythagorean theorem.
Use the law of sines instead when you have a matching side and opposite angle.
What You'll Practice
1
Finding side lengths in SAS triangles using two sides and the included angle
2
Calculating angles in SSS triangles when all three sides are known
3
Solving real-world bearing and navigation problems with non-right triangles
4
Determining ambiguous case scenarios and identifying multiple triangle solutions
Why This Matters
The Law of Cosines is essential for solving triangles that can't be handled with the Law of Sines. You'll use it in navigation, surveying, physics, and engineering to find distances and angles in non-right triangles, making it crucial for real-world problem-solving.
This Unit Includes
3 Video lessons
Learning resources
Skills
Law of Cosines
SAS Triangles
SSS Triangles
Trigonometry
Triangle Solving
Non-Right Triangles
Bearing Problems
NL Curriculum Aligned