Chapter 8.6, Problem 4CYU

To determine

To calculate:

The value of $x$

Answer to Problem 4CYU

The value of $x$ is $22.8$ .

Explanation of Solution

Given information:

  

Concept used:

Law of Sines:

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

Calculation:

  

With given one sided and two angles so use the law of Sines to write the proportion:

The angle opposite the side of the length $73$ has degree measure of ${180}^{\circ }-{141}^{\circ }-{18}^{\circ }={21}^{\circ }$ .

  $\frac{\sin 141}{x}=\frac{\sin 21}{13}$

Apply the property of cross products:

  $x\cdot \sin 21=13\cdot \sin 141$

Divide both sides by $\sin 21$ :

  $\begin{array}{l}x=\frac{13\cdot \sin 141}{\sin 21}\\ x=22.8\end{array}$

The value of $x$ is $22.8$ .