Trigonometry Section 6.1Trigonometry Section 6.1

Law of SinesLaw of Sines

Law of SinesLaw of Sines

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

Two forms of the law of sines:Two forms of the law of sines:

When to use the Law of SinesWhen 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 SSA, this is a difficult case because you can

have no solution, one, or two!have no solution, one, or two! Let’s do Example 1 on AASLet’s do Example 1 on AAS Let’s do Example 2 on ASALet’s do Example 2 on ASA

SSA Ambiguous Number of SSA Ambiguous Number of SolutionsSolutions

Any second solution must be 180 degrees Any second solution must be 180 degrees minus the angle that you got…why?minus the angle that you got…why?

One Solution Example 3One Solution Example 3 No Solution Example 4No Solution Example 4 Two Solutions Example 5Two Solutions Example 5 Let’s try some exercisesLet’s try some exercises

Area of Oblique TriangleArea of Oblique Triangle

Area=Area=

Why are these formulas correct?Why are these formulas correct? Example 6Example 6 Try finding the area of the following triangleTry finding the area of the following triangle

HomeworkHomework

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