Chapter 8.6, Problem 20PPS

To determine

To calculate:

The value of $x$ :

Answer to Problem 20PPS

The value of $x$ is $19.3$ .

Explanation of Solution

Given information:

  

Concept used:

Law of Sines:

  $a=b\frac{\sin \alpha }{\sin \beta }$

Calculation:

  

Since, the given two angles and one side set up a proportion using the Law of Sines:

The angle opposite side of the length $12$ has degree measure of ${180}^{\circ }-{118}^{\circ }-{39}^{\circ }={23}^{\circ }$ .

Law of Sines:

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

Put the values in equation (1):

  $\frac{\sin 23}{12}=\frac{\sin 39}{x}$

Apply the property of cross products:

  $x\cdot \sin 23=12\cdot \sin 39$

Divide both the sides by $\sin 23$ :

  $\begin{array}{l}x=\frac{12\sin 39}{\sin 23}\\ x\approx 19.3\end{array}$

The value of $x$ is $19.3$ .