Chapter 8.6, Problem 24PPS

To determine

To calculate:

The value of $x$ .

Answer to Problem 24PPS

The value of $x$ is $107.9$ .

Explanation of Solution

Given information:

Round angle measures to the nearest degree and side measures to the nearest tenth.

  

Concept used:

Law of cosines:

  $c^2=a^2+b^2-2ab\cos C$

Where,

  $a,b=$ sides

  $\cos C=$ angle

Calculation:

  

With the help of the diagram, it is observed that having the two sides and an included angle so, get the help of the Law of cosines to get the value of $x$ .

Law of cosines:

  $c^2=a^2+b^2-2ab\cos C$

Where,

  $\begin{array}{l}a=120\\ b=54\\ \cos C={64}^{\circ }\end{array}$

Consider $c^2$ as $x^2$ .

First substitute and then simplify,

  $x^2={\left(120\right)}^2+{\left(54\right)}^2-2\left(120\right)\left(54\right)\cos \left(64\right)$

Now simplify the,

  $x^2=11634.71$

Now take the square root of each side.

  $x=\sqrt{11634.71}$

Now simplify the under square root value

  $x\approx 107.9$

Hence the value of $x$ is $107.9$ .