Determine the number of possible triangles, abc, that can be formed given b = 45°, b = 4, and c = 5.

Given:
m∠B = 45°
b = 4
c = 5

From the Law of Sines, obtain

This yields
m∠A = 180 - 45 - 62.1 = 72.9°

The first triangle has
∠A=72.9°,  m∠B=45°,  m∠C = 62.1°,  a=5.41,  b=4,  c=5.

Also, 

This yields
m∠A = 180 - 45 - 117.9 = 17.1°

The second triangle has
m∠A = 17.1°,  m∠B = 45°,  m∠C = 117.9°,  a = 1.66,  b = 4,  c = 5

There are 2 possible triangles.