Answer:
[tex]14.1[/tex]
Step-by-step explanation:
Since we have two sides of a triangle and the angle between them, we can use the Law of Cosines.
For any triangle, the Law of Cosines states:
[tex]b^2=a^2+c^2-2ac\cos B[/tex], where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are all interchangeable.
Substituting given values, we have:
[tex]b^2=9^2+19^2-2(9)(19)\cos 45^{\circ},\\b^2=200.169480834,\\b\approx \boxed{14.1}[/tex]
