Question

Find the number of distinct triangles with the measurements a = 5, b =2, and a = 51 degrees.

Answer 1

The answer is the option b. 1.

Two sides and one angle determine one unique triangle.

If the angle is the between the two sides, you just can use the rule known as SAS, Side Angle Side.

When that is the case you use the cosine rule.

When the known angle is not between the two sides but one of the others, you use sine theorem.

Then in any case when you know two sides and one angle of a triangle the other side and angles are determined, which implies that there is only one possible triangle.