Trigonometry Section 6.1 Law of Sines

For a triangle, we will label the angles with capital letters A, B, C, and the sides with lowercase a, b, c where side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C. For a triangle, we will label the angles with capital letters A, B, C, and the sides with lowercase a, b, c where side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C. Two forms of the law of sines: Two forms of the law of sines:

When to use the Law of Sines AAS or ASA (two angles and one side) AAS or ASA (two angles and one side) SSA, this is a difficult case because you can have no solution, one, or two! SSA, this is a difficult case because you can have no solution, one, or two! Let’s do Example 1 on AAS Let’s do Example 1 on AAS Let’s do Example 2 on ASA Let’s do Example 2 on ASA

SSA Ambiguous Number of Solutions Any second solution must be 180 degrees minus the angle that you got…why? Any second solution must be 180 degrees minus the angle that you got…why? One Solution Example 3 One Solution Example 3 No Solution Example 4 No Solution Example 4 Two Solutions Example 5 Two Solutions Example 5 Let’s try some exercises Let’s try some exercises

Area of Oblique Triangle Area= Area= Why are these formulas correct? Why are these formulas correct? Example 6 Example 6 Try finding the area of the following triangle Try finding the area of the following triangle

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