Question

Help solve for b it is for trigonometry ​

Answer 1

Answer:

$b\approx 21.435332$

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:

$\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}$

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:

$\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}$

$\frac{sin(A)}{a}=\frac{sin(72)}{b}=\frac{sin(53)}{18}$

Remove the parts of the equation that are not relevant to the problem,

$\frac{sin(A)}{a}=\frac{sin(72)}{b}=\frac{sin(53)}{18}$

$\frac{sin(72)}{b}=\frac{sin(53)}{18}$

Take the cross product of the proportion,

$\frac{sin(72)}{b}=\frac{sin(53)}{18}$

$18(sin(72))=b(sin(53))$

Inverse operations,

$18(sin(72))=b(sin(53))$

$b=\frac{18(sin(72)}{sin(53)}$

$b\approx 21.435332$