Answer:
[tex]b=40.01\ units[/tex]
Step-by-step explanation:
we know that
Applying the law of sines
[tex]\frac{b}{sin(B)}=\frac{a}{sin(A)}[/tex]
[tex]b=\frac{a}{sin(A)}(sin(B))[/tex]
we have
[tex]a=25\ units[/tex]
[tex]A=32.5\°[/tex]
Find the measure of angle B
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
so
[tex]A+B+C=180\°[/tex]
substitute the given values
[tex]32.5\°+B+26.8\°=180\°[/tex]
[tex]B=180\°-59.3\°=120.7\°[/tex]
Find the length side b
[tex]b=\frac{a}{sin(A)}(sin(B))[/tex]
substitute the values
[tex]b=\frac{25}{sin(32.5\°)}(sin(120.7\°))[/tex]
[tex]b=40.01\ units[/tex]
