Question

TRIG ANALYSIS- THE LAW OF SINES- THE AMBIGUOUS CASERecall that your triangle should be set up so that angside b, and angle C is opposite side c.PLEASE HELP. WILL MARK BRAINLIEST

Answer 1

The sine law is described by the equation

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

1) Given angle C, length of side b, and length of side c, we are looking for the value of angle B. The angle B can be computed using

$\begin{gathered} \frac{\sin B}{b}=\frac{\sin C}{c} \\ \sin B=\frac{b}{c}\sin C \end{gathered}$

Substitute the values on the equation above and solve, we get

$\begin{gathered} \sin B=\frac{34}{31}\sin (65)=0.994 \\ B=\sin ^{-1}(0.994) \\ B=83.7 \end{gathered}$

Thus, angle B is equal to 83.7 degrees.

2) Given angle B, length of side a, and length of side b, we are looking for the value of angle A. The angle A can be computed using

$\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b} \\ \sin A=\frac{a}{b}\sin B \end{gathered}$

Substitute the values on the equation above and solve, we get

$\begin{gathered} \sin A=\frac{10}{5}\sin (126)=1.62 \\ A=\sin ^{-1}(1.62)=Error_{} \end{gathered}$

There are no valid measurements for angle A on this solution.

3) Given angle C, length of side c, and length of side b, we are looking for the value of angle B. The angle B can be computed using

$\begin{gathered} \frac{\sin B}{b}=\frac{\sin C}{c} \\ \sin B=\frac{b}{c}\sin C \end{gathered}$

Substitute the values on the equation above and solve, we get

$\begin{gathered} \sin B=\frac{22}{24}\sin (22)=0.3728 \\ B=\sin ^{-1}(0.3728)=21.9 \end{gathered}$

Thus, angle B is equal to 21.9 degrees.

4. Given angle A, length of side c, and length of side a, we are looking for the value of angle C. The angle C can be computed using

$\begin{gathered} \frac{\sin C}{c}=\frac{\sin A}{a} \\ \sin C=\frac{c}{a}\sin A \end{gathered}$

Substitute the values on the equation above and solve, we get

$\begin{gathered} \sin C=\frac{34}{32}\sin (64)=0.955_{} \\ C=\sin ^{-1}(0.955)=72.74 \end{gathered}$

Thus, angle C is equal to 72.74 degrees.

5. Given angle A, length of side c, and length of side a, we are looking for the value of angle C. The angle C can be computed using

$\begin{gathered} \frac{\sin C}{c}=\frac{\sin A}{a} \\ \sin C=\frac{c}{a}\sin A \end{gathered}$

Substitute the values on the equation above and solve, we get

$\begin{gathered} \sin C=\frac{9}{17}\sin (127)=0.4228 \\ C=\sin ^{-1}(0.4228)=25.0 \end{gathered}$

Thus, angle C is equal to 25.0 degrees.