1. Lesson: _____ Section 6.1 The Law of Sines
What do we call one of these?
Solve!
What does it mean when we say that two quantities are proportional?

2. The Law of Sines C b a h A B
applet

3. ex. B=110°, C=30, c=10.5, Solve the triangle!
The Law of Sines C b a
- or - A B c
ex. B=110°, C=30, c=10.5, Solve the triangle!

4. We need three pieces of information, one of which must be a side.
Solving Oblique (non-right) Triangles
We need three pieces of information, one of which must be a side.
4 cases are possible…
1.) 2 angles and any side
2.) 2 sides and an angle opposite one of the sides
3.) 3 sides
4.) 2 sides and their included angle
Law of Sines
Law of Cosines

5. The Law of Sines AMBIGUOUS CASE (SSA)
Three possible situations can occur
No such triangle exists
Exactly 1 triangle fits the description
Two different triangles both fit the description
What does “ambiguous” mean? Why is this called the “ambiguous” case?
Examples 3,4,5 from the text are good.
Ex.4.(No solutions): a = 15, b = 25, A = 85° Ex.3.(1 solution): a = 22, b = 12, A = 42° Ex.5.(2 solutions): a = 12, b = 31, A = 20.5°

6. If we are dealing with the SSA case (Ambiguous),
Use the Law of Sines to solve for .
Then set up 2 cases to represent both the acute case  and the obtuse case (180 - ).
Draw a diagram for each of these cases.
After solving each triangle, test to see that everything is ok.
Do the angles add to 180? Is the side-angle relationship preserved?

7. Area of an Oblique Triangle Formula
Area = ½ bc sinA = ½ ab sinC = ½ ac sinB
This is the same as Area = ½ bh Show why! A B C b a c h