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Solving Oblique Triangles

Oblique Triangle Review


The Law of Sines

An oblique triangle is a triangle with no right angle. An oblique triangle has either three acute angles, or one obtuse angle and two acute angles. In any case, as in any triangle, the sum of all three angles is equal to 180 degrees.

We will continue to go by our usual practice in this book of naming the three vertices of the triangle A , B , and C , and naming the sides opposite these vertices a , b , and c , respectively. An oblique triangle is determined, meaning it can be solved, if a side and any two other parts are known. Three basic situations fulfill this simple requirement: when two angles and a side are given, two sides and an angle are given, or three sides are given.

A special circumstance arises when two sides and their included angle are given. In such situation, the triangle is not always determined; this situation has garnered the name the ambiguous case, and is the only situation in which a side and two other parts of a triangle don't determine the triangle. In the next sections, we'll study the Law of Sines and the Law of Cosines, and each possible scenario.