Question

Help solve for b it is for trigonometry

​

Answer 1

`b\approx 21.435332`

Explanation:

The Law of Sines is a property that relates the sides and angles of any triangle. This property states the following:

`(sin(A))/(a)=(sin(B))/(b)=(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:

`(sin(A))/(a)=(sin(B))/(b)=(sin(C))/(c)`

`(sin(A))/(a)=(sin(72))/(b)=(sin(53))/(18)`

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

`(sin(A))/(a)=(sin(72))/(b)=(sin(53))/(18)`

`(sin(72))/(b)=(sin(53))/(18)`

Take the cross product of the proportion,

`(sin(72))/(b)=(sin(53))/(18)`

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

Inverse operations,

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

`b=(18(sin(72))/(sin(53))`

`b\approx 21.435332`