Question

Solve for the remaining angles and side of the triangle described below. Round to the nearest thousandth:B = 60°c = 5, a = 6

Answer 1

• Using the law of cosines:

b² = c² + a² - 2ac CosB

b² = 5² + 6² - 2(6)(5) cos 60°

b² = 31

b = 5.568

• Using the law of sines:

`\begin{gathered} \frac{b}{\sin\text{ B}}=\text{ }\frac{a}{\sin \text{ A}} \\ \\ \sin A\text{ =}(\sin B* a)/(b) \\ \\ \sin A\text{ =}\frac{\sin 60\text{\degree x 6}}{5.568} \\ \\ A\text{ =68.869\degree} \end{gathered}`

°C = 180° - 60° - 68.869° = 51.131°