Chapter 8.6, Problem 4ACYP

To determine

To calculate:

The value of $x$

Answer to Problem 4ACYP

The values of $x$ is $37.51$ .

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,

  $\begin{array}{l}c=JM=1.3\\ a=JK=2.1\\ b=KM=1.9\\ C=x\end{array}$

Put the values in equation (1)

  $\begin{array}{l}{\left(1.3\right)}^2={\left(2.1\right)}^2+{\left(1.9\right)}^2-2\left(2.1\right)\left(1.9\right)\cos x\\ 1.69=4.41+3.61-7.98\cos x\\ 1.69=8.02-7.98\cos x\\ 7.98\cos x=6.33\\ x=37.51\end{array}$

The values of $x$ is $37.51$ .