Two sides and an angle​ (SSA) of a triangle are given. Determine whether the given measurements produce one​ triangle, two​ triangles, or no triangle at all. Solve each triangle that results.

Question

a=7, b=6, A=70 degrees

What is B, C, and c?

Answer 1

Using the Law of Sines, sin70° / 7 = sinB / 6

So, sinB = 6sin70° / 7 = 0.80545

Since the sine function is positive in quadrants 1 and 2, there are 2 possibilities for angle B:

∠B = Sin^-1(0.80545) or 180° - Sin^-1(0.80545) = 53.65° or 126.35°

Since 126.35° + 70° is greater than 180°. only 53.65° is a valid choice for ∠B.

So, there is only 1 triangle.