The sine law: the ambiguous case (SSA)

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Learn it Given two sides and an angle not between them (SSA), there may be 0, 1 or 2 triangles. With angle A, side a opposite it and side b: h = b sin A. If a < h: none. a = h: one (right triangle). h < a < b: two. a ≥ b: one.

Example: A = 40°, a = 8, b = 10. How many triangles?

h = 10 sin 40° ≈ 6.43.
6.43 < 8 < 10: two triangles.

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