Chapter 8.6, Problem 3ACYP

To determine

To calculate:

The value of $x$

Answer to Problem 3ACYP

The values of $x$ is $30.19$ .

Explanation of Solution

Given information:

  

Concept used:

Law of Cosines:

  $c^2=a^2+b^2-2ab\cos C$

Calculation:

  

  $x$ : The length of third side of the triangle.

Since, the given two sides and one angles, setup the proportion using the Law of Cosines for $x$ :

Law of Cosines:

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

Where,

  $\begin{array}{l}c=DF=x\\ a=DG=15\\ b=GF=19\\ C=125\end{array}$

Put the values in equation (1)

  $\begin{array}{l}{x}^2={\left(15\right)}^2+{\left(19\right)}^2-2\left(15\right)\left(19\right)\cos 125\\ x^2=225+361-570\cos 125\\ x^2=586-\left(-326\right)\\ x^2=912\\ x=30.19\end{array}$

The values of $x$ is $30.19$ .