Chapter 12.9, Problem 1MRE

To determine

Find the length $\left(c\right)$ of triangle ABC to three significant digits such that $a=8,b=5\text{ and }\angle C=62°$ .

Answer to Problem 1MRE

The length $\left(c\right)$ is equal to $7.17$ .

Explanation of Solution

Given information: The given triangle ABC has $a=8,b=5\text{ and }\angle C=62°$ .

Calculation: By using the law of cosines $c^2=a^2+b^2-2ab\cos C$ the value of $\left(c\right)$ is evaluated as,

  $\begin{array}{c}{c}^2={\left(8\right)}^2+{\left(5\right)}^2-2\left(8\right)\left(5\right)\cos \left(62°\right)\mathrm{....}\left(\begin{array}{l}\text{Plugging }a=8,b=5\\ \text{and }\angle C=62°\end{array}\right)\\ c=\pm \sqrt{64+25-80\cos \left(62°\right)}\\ c=\pm 7.172\\ c=7.17\mathrm{....}\left(\text{Neglect negative length}\right)\end{array}$

Hence the length $\left(c\right)$ is equal to $7.17$ .