Chapter 8.6, Problem 5CYU

To determine

To calculate:

The value of $x$

Answer to Problem 5CYU

The value of $x$ is $21$ .

Explanation of Solution

Given information:

  

Concept used:

Law of Cosines:

  $c^2=a^2+b^2-2ab\cos C$

Calculation:

  

With given the measures of two sides and included angle, then use the law of Cosines to solve the problem.

Law of Cosines:

  $c^2=a^2+b^2-2ab\cos C\mathrm{...}\left(1\right)$

Where,

  $\begin{array}{l}a=14.7\\ b=7\\ C=18\\ c=x\end{array}$

Put the values in equation (1)

  $\begin{array}{l}{x}^2=a^2+b^2-2ab\cos C\\ x^2={\left(14.7\right)}^2+{\left(7\right)}^2-2\left(14.7\right)\left(2\right)\cos \left(18\right)\\ x^2=216.09+49-195.73\\ x^2=69.36\\ x\approx 21\end{array}$

The value of $x$ is $21$ .