How do I know that how many triangles are formed

Hi,

I am a bit confused about number of triangles for example: Determine the number of Triangles with the given parts:
a=11
b=6
c=8
Ans: 1 triangle
or
B= 65.7 deg
b= 4.42
a=17.5
Ans: No solution

I know how to find the other angles by using law of sines and cosins. I mean in both questions a > b. So how in first question one triangle is formed and in the second no Triangle is formed? Please explain. Thanks.

When you use the Sine Law to calculate the sine of the angle opposite side a, the answer is 3.6+
The sine of an angle must be between -1 and +1 inclusive.
Therefore the angle opposite a does not exist ==> no triangle.