1. Law of Sines and Law of Cosines
Advanced Geometry

2. Law of Sines and Law of Cosines
When do we need to use these laws?

3. Law of Sines

4. When can we use Law of Sines?
You can use the Law of sines to solve a triangle if you know…
2 angles and any side (ASA or AAS)

5. Law of Cosines

6. When can we use Law of Cosines?
You can use the Law of cosines to solve a triangle if you know…
The lengths of all 3 sides (SSS)
2 sides and the included angle (SAS)

7. Examples – Solve for x.
1. 2.

8. Solve the triangle below.

9. Special Case
In ∆PQR, if m∠Q = 39, PQ = 41, and PR = 28, find m∠R.

10. Sometimes there are two answers!
Imagine we know angle A, and sides a and b (SSA). We can swing side a to left or right and come up with two results (a small triangle and a much wider triangle) Both answers are right!

11. Special Case
This only happens if we know two sides and an angle not included, and even then not always, but we have to watch out for it.

12. How do we find the other answer?
We can take our first answer and subtract it from 180 to find the other possible answer.

13. Both Solutions

14. Special Case
Are there 2 answers for ∠B in this triangle?