Law of SInes

How many distinct triangles can be formed for which m∠E = 64°, g = 9, and e = 10?

1 triangle

In △MNO, m = 20, n = 14, and m∠M = 51°. How many distinct triangles can be formed given these measurements? There are no triangles possible. There is only one distinct triangle possible, with m∠N ≈ 33°. There is only one distinct triangle possible, with m∠N ≈ 147°. There are two distinct triangles possible, with m∠N ≈ 33° or m∠N ≈ 147°.

There is only one distinct triangle possible, with m∠N ≈ 33°.

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

When the third side of the triangle is too short to intersect the other side, no triangles can be formed. When the third side is just long enough to meet the other side at one point, one triangle is formed. When the third side is long enough to intersect the other side at two points, two triangles are formed

How many distinct triangles can be formed for which m∠J = 129°, k = 8, and j = 3?

Zero (0) triangle