Chapter 8.7, Problem 51SPR

To determine

To calculate:

The value of $x$ nearest to the tenth.

Answer to Problem 51SPR

The value of $x$ is $50.6$ .

Explanation of Solution

Given information:

  

Formula used:

Law of Sines:

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

Calculation:

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

  $\frac{\sin 21}{23}=\frac{\sin 128}{x}$

Apply the property of cross products:

  $x\sin 21=23\sin 128$

Divide both sides by $\sin \left(19\right)$ :

  $\begin{array}{l}x=\frac{23\sin 128}{\sin 21}\\ x=50.6\end{array}$

Hence, the value of $x$ is $50.6$ .