Chapter 8.6, Problem 25PPS

To determine

To calculate:

The value of $x$ .

Answer to Problem 25PPS

The value of $x$ is ${98}^{\circ }$ .

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,

  $\begin{array}{l}a=29\\ b=50\\ c=61\end{array}$

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

First substitute and then simplify,

  ${\left(61\right)}^2={\left(29\right)}^2+{\left(50\right)}^2-2\left(29\right)\left(50\right)\cos \left(x\right)$

Now simplify the,

  $3721=841+2500-2900\cos \left(x\right)$

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

  $-0.13103=\cos \left(x\right)$

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

  $x\approx 98$

Hence the value of $x$ is ${98}^{\circ }$ .