Question

there are two possible triangles with the measures given. complete the steps to solve the triangles.
b = 18.7, c = 16.1, c = 35°
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 ) } \\)
from least to greatest, what are the possible measures of angle b? round to the nearest whole number.
____ and ____

Explanation:

Step1: Solve for \(\sin B\)

From the equation \(\frac{16.1}{\sin(35^{\circ})}=\frac{18.7}{\sin(B)}\), we can cross - multiply to get \(16.1\times\sin(B)=18.7\times\sin(35^{\circ})\). Then \(\sin(B)=\frac{18.7\times\sin(35^{\circ})}{16.1}\).
We know that \(\sin(35^{\circ})\approx0.5736\), so \(\sin(B)=\frac{18.7\times0.5736}{16.1}\approx\frac{10.7263}{16.1}\approx0.6663\).

Step2: Find the first value of \(B\)

Using the inverse - sine function \(B_1=\sin^{- 1}(0.6663)\approx42^{\circ}\).

Step3: Find the second value of \(B\)

Since \(\sin\theta=\sin(180^{\circ}-\theta)\), the second value of \(B\) is \(B_2 = 180^{\circ}-42^{\circ}=138^{\circ}\).

Answer:

\(42\) and \(138\)