Question

Solve the triangle. a=1, b=9, C=60 degrees Find the approximation of c≈A≈B≈

Answer 1

Use the cosine law to find the length of side c:

$c^2=a^2+b^2-2ab\cos C$$\begin{gathered} c^2=1^2+9^2-2(1)(9)\cos 60 \\ c^2=1+81-18\cos 60 \\ c^2=82-18\cos 60 \\ c^2=82-9 \\ c^2=73 \\ c=\sqrt[]{73} \\ c\approx8.54 \end{gathered}$

Use the cosine law to find the measure of angles A or B:

$\begin{gathered} \\ \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\ \\ To\text{ find angle A:} \\ \frac{\sin A}{a}=\frac{\sin C}{c} \\ \\ \frac{\sin A}{1}=\frac{\sin 60}{\sqrt[]{73}} \\ \\ \sin A=\frac{\sin 60}{\sqrt[]{73}} \\ \\ A=\sin ^{-1}(\frac{\sin60}{\sqrt[]{73}}) \\ \\ A\approx5.82º \end{gathered}$