Law of Sines and Ambiguous Cases Worksheets
What is the Law of Sines and the Ambiguous Cases? We are aware of the generic law of sines which are used in figuring out the unknown values of the sides or angles in a triangle. However, some cases make it hard for the generic law of sines to be effective. The ambiguous case occurs when one uses the law of sines to find out the missing parameters of a triangle. The known parameters are two sides and an angle opposite one to those angles, making it an SSA triangle. Thus, for the ambiguous cases, three possible situations are possible, which are given below. No triangle with the given information exists. One such triangle exists. Two distinct triangles may be formed which can satisfy the original law of sines conditions.
Joseph J Sylvester (1814 to 1897)
The early study of Euclid made me a hater of geometry.