Chapter 8.6, Problem 27PPS

To determine

To calculate:

The value of $x$ .

Answer to Problem 27PPS

The value of $x$ is ${112}^{\circ }$ .

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 three sides and no angles get the help of the law of cosines, to calculate the value of $x$ .

Law of cosines:

  $c^2=a^2+b^2-2ab\cos C$

Where,

  $\begin{array}{l}a=1.8\\ b=5.6\\ c=6.5\end{array}$

And $\cos C=x^{\circ }$

First substitute and then simplify,

  ${\left(6.5\right)}^2={\left(1.8\right)}^2+{\left(5.6\right)}^2-2\left(1.8\right)\left(5.6\right)\cos \left(x\right)$

Now simplify the,

  $42.25=3.24+31.36-20.16\cos \left(x\right)$

Now solve for the $\cos \left(x\right)$

  $-0.3795=\cos \left(x\right)$

Now use the invers cosine ratio, the value of $x$ is,

  $x\approx 112$

Hence the value of $x$ is ${112}^{\circ }$ .