Chapter 8.6, Problem 12PPS

To determine

To calculate:

The value of $x$ :

Answer to Problem 12PPS

The value of $x$ is $35.1$ .

Explanation of Solution

Given information:

  

Concept used:

Law of Cosines:

  $c^2=a^2+b^2-2ab\cos C$

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):

  $\frac{\sin 47}{x}=\frac{\sin 30}{24}$

Apply the property of cross products:

  $x\cdot \sin 30=24\cdot \sin 47$

Divide both the sides by $\sin 30$ :

  $\begin{array}{l}x=\frac{24\sin 47}{\sin 30}\\ x=35.1\end{array}$

The value of $x$ is $35.1$ .