Chapter 12.9, Problem 2ST

To determine

Find the side $\left(f\right)$ in triangle DEF such that $d=18\text{,}e=24\text{ and }\angle F=42°$ .

Answer to Problem 2ST

The length of side $\left(f\right)$ is $16.1$ .

Explanation of Solution

Given information: The given triangle DEF has $d=18\text{,}e=24\text{ and }\angle F=42°$ .

Calculation: Since the triangle DEF has $d=18\text{,}e=24\text{ and }\angle F=42°$ . Therefore by law of cosine in triangle DEF,

  $\begin{array}{c}{f}^2=d^2+e^2-2de\cos \left(F\right)\\ f^2={\left(18\right)}^2+{\left(24\right)}^2-2\left(18\right)\left(24\right)\cos \left(42\right)\mathrm{....}\left\{\begin{array}{l}d=18\text{,}e=24\\ \text{and }\angle F=42°\end{array}\right\}\\ f=\pm \sqrt{{\left(18\right)}^2+{\left(24\right)}^2-2\left(18\right)\left(24\right)\cos \left(42\right)}\\ f\approx 16.1\mathrm{....}\left(\text{Take positive value}\right)\end{array}$

Hence the length of side $\left(f\right)$ is $16.1$ .