Chapter 8.6, Problem 26PPS

To determine

To calculate:

The value of $x$ .

Answer to Problem 26PPS

The value of $x$ is ${72}^{\circ }$ .

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,

  $\begin{array}{l}a=26.2\\ b=13.5\\ c=25.4\end{array}$

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

First substitute and then simplify,

  ${\left(25.4\right)}^2={\left(26.2\right)}^2+{\left(13.5\right)}^2-2\left(26.2\right)\left(13.5\right)\cos \left(x\right)$

Now simplify the,

  $645.16=686.44+182.25-7074\cos \left(x\right)$

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

  $0.3160=\cos \left(x\right)$

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

  $x\approx 72$

Hence the value of $x$ is ${72}^{\circ }$ .