Chapter 12.9, Problem 5ST

To determine

Find the area of triangle RST such that $r=9,s=12\text{ and }\angle T=53.7°$ .

Answer to Problem 5ST

The area $\left(A\right)$ of triangle RST is $43.5\text{ sq}\text{. units}$ .

Explanation of Solution

Given information: The given triangle RST has $r=9,s=12\text{ and }\angle T=53.7°$ .

Calculation: Since the given triangle RST has $r=9,s=12\text{ and }\angle T=53.7°$ . And the given triangle has the case of side-angle-side where the given angle $\left(\angle T=53.7°\right)$ is included angle between the given two sides $r=9\text{ and }s=12$ . Therefore area $\left(A\right)$ of triangle RST is evaluated as,

  $\begin{array}{c}A=\frac{1}{2}rs\sin T\\ =\frac{1}{2}\left(9\right)\left(12\right)\sin \left(53.7\right)\mathrm{....}\left\{\begin{array}{l}r=9,s=12\text{ and}\\ \angle T=53.7°\end{array}\right\}\\ =43.5\text{ sq}\text{. units}\end{array}$