Equations · Algebra and geometry
Law of cosines
The third side of any triangle from two sides and the angle between them.
c² = a² + b² − 2ab cos γ
Aethel says
c squared equals a squared plus b squared minus 2 a b cos gamma
What it says
For any triangle with sides a, b and c, where γ is the angle opposite side c, the square of c equals the sum of the squares of a and b, less a correction that depends on the angle.
When γ is a right angle its cosine is zero and the formula becomes the Pythagorean theorem. A wider angle makes c longer, a narrower one makes it shorter.
Symbol by symbol
| Symbol | Say it | Means |
|---|---|---|
| a, b, c | a, b, c | the lengths of the three sides |
| γ | gamma | the angle opposite side c, between sides a and b |
| cos | cos, or cosine | the cosine of the angle |
More onγGamma
Where you meet it
Trigonometry, surveying and navigation, and the geometry of vectors.
Questions
How do you say Law of cosines out loud?
c² = a² + b² − 2ab cos γ is read: “c squared equals a squared plus b squared minus 2 a b cos gamma.” That is exactly what Aethel says when it meets the formula in a book.
What does a, b, c mean in Law of cosines?
a, b, c (said “a, b, c”) is the lengths of the three sides.
What does γ mean in Law of cosines?
γ (said “gamma”) is the angle opposite side c, between sides a and b.
Can I listen to the equations in my own textbook like this?
Yes. Upload a PDF, EPUB or text file and Aethel reads it aloud with every equation spoken as maths, the way it reads this one, and highlights each sentence as it goes. You can start free.