Question

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

Answers:
0
1
2

and please help explain if possible thanks

Answer 1

There are 2 triangles here. You have to drop an altitude and determine the length of it. You can use the fact that sin45 = h/5 (h is the height) and get that the height is 3.5. The rule then is if h is smaller than b which is in turn smaller than c, you have 2 triangles. This is the case of the ambiguous triangle, that SSA that you cannot use to prove congruency. The rules are very particular for whether or not 0, 1, or 2 triangles exist. Learn them.