Chapter 5.6, Problem 15E

To determine

To solve: Triangle $a=8.2,B={24.8}^{\circ },C={61.3}^{\circ }$ . Round to the nearest tenth

Answer to Problem 15E

  $\angle A={93.9}^{\circ },c=7.2,b=3.4$

Explanation of Solution

Given information: $a=8.2,B={24.8}^{\circ },C={61.3}^{\circ }$

Calculation:

  $\angle A=180-\left(24.8+61.3\right)={93.9}^{\circ }$

Law if sines:

  $\begin{array}{l}\frac{8.2}{\sin {93.9}^{\circ }}=\frac{b}{\sin {24.8}^{\circ }}=\frac{c}{\sin {61.3}^{\circ }}\\ b=\frac{8.2\times \sin {24.8}^{\circ }}{\sin {93.9}^{\circ }}=3.4\\ c=\frac{8.2\times \sin {61.3}^{\circ }}{\sin {93.9}^{\circ }}=7.2\end{array}$

Thus,

  $\angle A={93.9}^{\circ },c=7.2,b=3.4$