Solve the triangles

Question

Two sides and an angle are given below. Determine whether the given information results in one​ triangle, two​ triangles, or no triangle at all. Solve any​ triangle(s) that results. a=8, b=3, A=60degrees

Answer 1

a = 8 b= 3

A = 60°

As the sin law tells us sin A/a = sin B/b,

Then, B = sin-1(sin 60° * 3/8) = 18.95°

Note that the supplementary angle to B, which has the same value of sin, is not possible (in fact, you can show that, when given the angle opposite the longer side, there always be only one set of angles possible).

Then, the third angle will be 180° - 60° - 18.95° = 101.05°. Thus, the length of the third side is

8 sin 101.05°/sin 60° = 9.07.