Question

measures given. complete the steps to solve the triangles.

( b = 18.7, c = 16.1, c = 35 ^ { circ } )

which equation can you use to find the measure of angle ( b )?

( \frac { 16.1 } { sin ( 35 ^ { circ } ) } = \frac { 18.7 } { sin ( b ) } )

( \frac { 18.7 } { sin ( 35 ^ { circ } ) } = \frac { 16.1 } { sin ( b ) } )

( \frac { 18.7 } { 16.1 } = \frac { sin ( 35 ^ { circ } ) } { sin ( b ) } )

Explanation:

Step1: Recall the Law of Sines

The Law of Sines states that in a triangle, \(\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}\).

Step2: Substitute the given values

Given \(b = 18.7\), \(c=16.1\), and \(C = 35^{\circ}\). According to the Law of Sines \(\frac{b}{\sin(B)}=\frac{c}{\sin(C)}\), substituting the values we get \(\frac{18.7}{\sin(B)}=\frac{16.1}{\sin(35^{\circ})}\), which can be rewritten as \(\frac{16.1}{\sin(35^{\circ})}=\frac{18.7}{\sin(B)}\).

Answer:

\(\frac{16.1}{\sin(35^{\circ})}=\frac{18.7}{\sin(B)}\) (the first option)