Chapter 8.6, Problem 14PPS

To determine

To calculate:

The value of $x$ :

Answer to Problem 14PPS

The value of $x$ is $7.7$ .

Explanation of Solution

Given information:

  

Concept used:

Law of Sines:

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

Calculation:

  

Since, the given two angles and non included sides set up a proportion using the Law of Sines:

Law of Sines:

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

Put the values in equation (1):

  $\frac{\sin 67}{x}=\frac{\sin 73}{8}$

Apply the property of cross products:

  $x\cdot \sin 73=8\cdot \sin 67$

Divide both the sides by $\sin 73$ :

  $\begin{array}{l}x=\frac{8\sin 67}{\sin 73}\\ x\approx 7.7\end{array}$

The value of $x$ is $7.7$ .