Answer:
[tex]b\approx 21.435332[/tex]
Step-by-step explanation:
The Law of Sines is a property that relates the sides and angles of any triangle. This property states the following:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
Where (A), (B), and (C) are the angles of the triangles. The sides (a), (b), and (c) are the sides opposite their respective angles, (side (a) is the opposite angle (<A); side (b) is the opposite angle (<B); and side (c) is the opposite angle (<C)). Substitute the given information into the formula and solve for the unknown:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
[tex]\frac{sin(A)}{a}=\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]
Remove the parts of the equation that are not relevant to the problem,
[tex]\frac{sin(A)}{a}=\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]
[tex]\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]
Take the cross product of the proportion,
[tex]\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]
[tex]18(sin(72))=b(sin(53))[/tex]
Inverse operations,
[tex]18(sin(72))=b(sin(53))[/tex]
[tex]b=\frac{18(sin(72)}{sin(53)}[/tex]
[tex]b\approx 21.435332[/tex]
