114373
AssignmentLong Text

Law of Sines (Sec 8-3)

Question 114373 • Fall 24 GMS Geometry: Concepts and Connections B

When using the law of sines, why can the SSA case result in zero, one, or two triangles? Explain.

Answer

Answer:

The SSA case is known as the ambiguous case because the given dimensions do not always uniquely determine a single triangle. If the side opposite the given angle is shorter than the altitude of the triangle, no triangle can be formed. If the side is exactly equal to the altitude or is longer than or equal to the other given side, only one triangle is formed. If the side is longer than the altitude but shorter than the adjacent side, it can intersect the third side at two different points, creating two distinct triangles.

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