We have the next given information for the given triangle:
∠A= 25 degrees
∠C = 55 degrees
and
AB=60
To solve this, we need to use the Law of sines, which is given by:
[tex]\frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}[/tex]Where ab= b = 60
Solve for a:
[tex]\frac{\sin(A)}{a}=\frac{\sin(B)}{b}[/tex][tex]a=\frac{\sin (A)}{\frac{\sin (B)}{b}}[/tex][tex]a=\frac{b\cdot\sin (A)}{\sin (B)}[/tex]Replacing the values:
[tex]a=\frac{60\cdot\sin (25)}{\sin (55)}[/tex]Then:
[tex]a\approx31[/tex]Now, we need to find the side lenght of c
