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.
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