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The Law of Sines: The Ambiguous Case

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The Ambiguous Case of the Law of Sines is when we are given two sides, a and b, and one angle, alpha, opposite one of those sides ( SSA ). In this video I explain all four possibilities, depending on the sizes of the two given sides: 1) No solution (no triangle possible) 2) A unique solution which is a right triangle 3) Two solutions or 4) One solution which is not a right triangle.

We apply the law of sines to the two given sides a and b, the given angle alpha, and the other angle, beta, opposite to the other side. If sine of beta gives us something outside the interval [-1,1], there is no solution. If sine of beta gives us equal to 1, there is a unique solution which is a right triangle. If sine of beta is a number greater than zero and less than one, we could have two solutions or one which is not a right triangle.

Watch the video. Watching the video is a lot easier than following this explanation.