Chapter 8.6, Problem 4BCYP

To determine

To calculate:

The value of $x$

Answer to Problem 4BCYP

The values of $x$ is $72.85$ .

Explanation of Solution

Given information:

  

Concept used:

Law of Cosines:

  $c^2=a^2+b^2-2ab\cos C$

Calculation:

  

  $x$ : The angle of the triangle.

Since, the given three sides 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,

  $\begin{array}{l}c=RT=6.1\\ a=RS=4.5\\ b=ST=3\\ C=x\end{array}$

Put the values in equation (1)

  $\begin{array}{l}{\left(6.1\right)}^2={\left(4.5\right)}^2+{\left(3\right)}^2-2\left(4.5\right)\left(3\right)\cos x\\ 37.21=20.25+9-27\cos x\\ 37.21=29.25-27\cos x\\ 27\cos x=-7.96\\ \cos x=-0.294\\ x=72.85\end{array}$

The values of $x$ is $72.85$ .