Question

Solve each triangle using either the Law of Sines or the Law of Cosines

$A=50°.B=55°,c=9$

Short answer

The required triangle is

$$\begin{gathered} C=75° \\ a=7.14 \\ b=7.63 \end{gathered}$$

Step-by-step solution

Given information

$A=50°.B=55°,c=9$

To find the angle C and sides a and b

Calculation

$$\begin{gathered} Weknow, \\ A+B+C=180° \\ \Rightarrow 50+55+C=180 \\ \Rightarrow C=180-50-55 \\ =75° \end{gathered}$$

$$\begin{gathered} FromLawofSines, \\ \frac{\sin A}{a}=\frac{\sin C}{c} \\ \Rightarrow \frac{\sin 50}{a}=\frac{\sin 75}{9} \\ \Rightarrow a=\frac{9\sin 50}{\sin 75} \\ =7.14 \\ \frac{\sin B}{b}=\frac{\sin C}{c} \\ \Rightarrow \frac{\sin 55}{b}=\frac{\sin 75}{9} \\ \Rightarrow b=\frac{9\sin 55}{\sin 75} \\ =7.63 \end{gathered}$$