Chapter 6.6, Problem 4E

To determine

To find: The triangle’s side $x$ using law of Cosines.

Answer to Problem 4E

The triangle has $x=26.76$ .

Explanation of Solution

Given information:

The given sidesand angles of the triangle are,

  $\begin{array}{l}A=108°\\ AC=15\\ AB=18\end{array}$

Concept used:

Law of Cosines:

If ABC is a triangle with sides $AC$ , $AB$ , and $BC$ , then

  $\cos A=\frac{A{C}^2+A{B}^2-B{C}^2}{2\left(AC\right)\left(AB\right)}$

The side $x$ of triangle is calculated as,

  $\begin{array}{l}\cos A=\frac{A{C}^2+A{B}^2-B{C}^2}{2\left(AC\right)\left(AB\right)}\\ \cos \left(108°\right)=\frac{{15}^2+{18}^2-x^2}{2\left(15\right)\left(18\right)}\\ -0.31=\frac{225+324-x^2}{540}\\ 225+324-x^2=-167.4\end{array}$

Simplify further,

  $\begin{array}{l}{x}^2=716.4\\ x=26.76\end{array}$

Therefore, the side $x$ of triangle is $x=26.76$ .