Question

Triangle ABC has the given measures. Solve the triangle(s), if any exist.

Answer 1

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:
$\frac{SinB}{b} = \frac{SinA}{a}$
$\frac{SinB}{4} = \frac{Sin(162)}{6.1}$
$SinB= \frac{4Sin(162)}{6.1}$
$B=arcSin(\frac{4Sin(162)}{6.1})$
$B=11.7$°

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°:
$C=180-(162+11.7)$
$C=180-173.7$
$C=6.3$

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

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