Triangle ABC has the given measures. Solve the triangle(s), if any exist. A = 162°, a = 6.1, b = 4How many triangle(s) can possibly be formed?

Since A>90° and a>b, we can only form one triangle.
Lest solve it:
First we are going to use the law of sine to find the angle B:
[tex] \frac{SinB}{b} = \frac{SinA}{a} [/tex]
[tex]\frac{SinB}{4} = \frac{Sin(162)}{6.1}[/tex]
[tex]SinB= \frac{4Sin(162)}{6.1} [/tex]
[tex]B=arcSin(\frac{4Sin(162)}{6.1})[/tex]
[tex]B=11.7[/tex]°

To find angle C, we are going to take advantage of the fact that the sum of the interior angels of a triangle is 180°:
[tex]C=180-(162+11.7)[/tex]
[tex]C=180-173.7[/tex]
[tex]C=6.3[/tex]

To find the remaining side c, we are going to use the law of sines:
[tex] \frac{c}{SinC} = \frac{a}{SinA} [/tex]
[tex] \frac{c}{Sin(6.3)} = \frac{6.1}{Sin(162)} [/tex]
[tex]c= \frac{6.1Sin(162)}{Sin(6.3)} [/tex]
[tex]c=3.6[/tex]

We can conclude that we can only form a triangle with the given measures.