Answer:
A. m<C = 57 degrees, a = 12, b = 19
Step-by-step explanation:
First we can start by calculating Angle C by using the rule that all interior angles of a triangle always add to 180 degrees:
180 - (39+84) = C
180 - 123 = C
C = 57
Now let's calculate side a. We can do this by using the sin rule: [tex]\frac{sin A}{a}=\frac{sin C}{c}[/tex]
According to the diagram we know that Angle A is 39 degrees, Angle C is 57 degrees, and side c is 16 so we can substitute these values into the formula and solve:
[tex]\frac{sin39}{a} =\frac{sin 57}{16} \\\\\frac{0.629320}{a} =\frac{0.838671}{16}\\\\0.629320=0.052417a\\0.629320/0.052417=a\\a= 12[/tex]
We can use the same method to solve for side b:
[tex]\frac{sin84}{b} =0.052417 \\0.994522=0.052417b\\0.994522/0.052417=b\\b= 19[/tex]
We now have the following values:
Angle C = 57 degrees, a = 12, b = 19
We can now see that A/Number 1 is the correct option.
Hope this helped!
