Determine whether the given information results in one triangle, two triangles, or no triangle at all.

Question

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results.

a = 3,    b = 2,     A = 50^o

Answer 1

Applying sine rule in the given triangle:

a/sinA = b/sinB

sinB = b*sinA/a =2*sin50/3 =0.511

B1 = 30.73 ; B2 = 180 - 30.73 = 149.27 deg

Angle C1 = 180 - A- B1 = 99.27 deg

Angle C2 = 180 -A -B2 =- 19.27 deg

Not possibe

So only one triangle possible.