Chapter 8.6, Problem 2CYU

To determine

To calculate:

The value of $x$

Answer to Problem 2CYU

The value of $x$ is $37.2$ .

Explanation of Solution

Given information:

  

Concept used:

Law of Sines:

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

Calculation:

  

With given the measure of the two angles and non included sides, so use the law of Sines to write the proportion:

  $\frac{\sin 135}{x}=\frac{\sin 20}{18}$

Apply the property of cross products:

  $x\cdot \sin 20=18\cdot \sin 135$

Divide both sides by $\sin 20$ :

  $\begin{array}{l}x=\frac{18\cdot \sin 135}{\sin 20}\\ x=37.2\end{array}$

The value of $x$ is $37.2$ .