Chapter 8.6, Problem 8CYU

To determine

To calculate:

The each triangle

Answer to Problem 8CYU

The angles are $AB=7.8,BC=4.4,m\angle B={77}^{\circ }$ .

Explanation of Solution

Given information:

  

Calculation:

  

The sum of angles of the triangle is $180$ .

  $m\angle B=180-\left(32+71\right)=77$

Since, the given angles and the side, setup the proportion using the Law of Sines:

Law of Sines:

  $a=b\frac{\sin \alpha }{\sin \beta }\mathrm{...}\left(1\right)$

Put the values in equation (1)

  $\frac{\sin 32}{BC}=\frac{\sin 77}{8}$

Apply the formula of cross product:

  $BC\cdot \sin 77=8\cdot \sin 32$

Divide both the sides by $\sin 77$

  $\begin{array}{l}BC=\frac{8\sin 32}{\sin 77}\\ BC=4.4\end{array}$

Put the values in equation (1)

  $\frac{\sin 77}{8}=\frac{\sin 71}{AB}$

Apply the formula of cross product:

  $AB\cdot \sin 77=8\cdot \sin 71$

Divide both the sides by $\sin 77$

  $\begin{array}{l}AB=\frac{8\sin 71}{\sin 77}\\ AB=7.8\end{array}$

The angles are $AB=7.8,BC=4.4,m\angle B={77}^{\circ }$ .