Most of you are probably familiar with "solving" right triangles (i.e., finding missing side lengths or angle measures of right triangles). The law of sines provides a technique for solving triangles that have no right angles (called oblique triangles). Specifically, the law of sines can be used to solve an oblique triangle when two angles and any side are given (AAS or ASA) or when two sides and an angle opposite one of them (SSA) are given. (This last case is sometimes referred to as the "ambiguous case". This will be discussed in more detail later.)
The Law of Sines:
Given triangle ABC with side a opposite angle A, side b opposite angle B and side c opposite angle C, the following relationship is true:
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Click here for a GSP 4.0 sketch to investigate/explore:
Before discussing this topic further,
you might wish to try solving a couple of oblique triangles using
the law of sines.
Example #1: Solve for angle A, side a and side c.
Example #2: A pole tilts toward the sun at an 8 degree angle from vertical, and it casts a 22-foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is 43 degrees. How tall is the pole?
