6.1 - Law of Sines

In the previous chapter we learned how to solve right triangles using trigonometry. Chapter 6 shows us how to solve for non-right triangles or otherwise known as oblique triangles.

To solve an oblique triangle, you need to know the measure of at least one side and any two other parts of the triangle - two sides, two angles, or one angle and one side. This breaks down into the following four cases

1. Two angles and any side (AAS or ASA)
2. Two sides and an angle opposite one of them (SSA)
3. Three sides (SSS)
4. Two sides and their included angle (SAS)

Below is how to derive the Law of Sines:

There are also an Ambiguous Case (SSA) in which there could be 2, 1, or no answer(s).

Below is a table to help determine the number of solutions there will be:

Area of an Oblique Triangle

Each triangle has a height of  h = b sinA and area of a triangle is A = 1/2*b*h

So, Area = 1/2 (c)(b sinA) = 1/2 bc sinA

You can also develop that: Area = 1/2 bc sinA = 1/2 ab sinC = 1/2 ac sinB