Chapter 8.6, Problem 3CYU

To determine

To calculate:

The value of $x$

Answer to Problem 3CYU

The value of $x$ is $69.8$ .

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 ${180}^{\circ }-{60}^{\circ }-{55}^{\circ }={65}^{\circ }$ .

  $\frac{\sin 60}{x}=\frac{\sin 65}{73}$

Apply the property of cross products:

  $x\cdot \sin 65=73\cdot \sin 60$

Divide both sides by $\sin 65$ :

  $\begin{array}{l}x=\frac{73\cdot \sin 60}{\sin 65}\\ x=69.8\end{array}$

The value of $x$ is $69.8$ .