Question

In $\text{△RST}$, $t=9.5$ inches, $\angle R=149°$ and $\angle S=12°$.

Find the length of $r$, to the nearest ${10}^{th}$ of an inch.

Answer 1

Finding the length of $r$, to nearest ${10}^{th}$ of an inch:

Given data,

In $\text{△RST}$,

$t=9.5$ inches,

$\angle R=149°$

$\angle S=12°$

Step-1: Finding the measure of $\angle T$.

Use the Law of Sines to find a missing angle measure

$$\begin{gathered} \mathrm{m}\angle \mathrm{T}=180-\left(12+149\right) \\ \mathrm{m}\angle \mathrm{T}=180-161 \\ \mathrm{m}\angle \mathrm{T}=19° \end{gathered}$$

Step-2: Find the length of $r$

Using the sine law in $\text{△RST}$ we can write,

$\begin{array}{rcl}\frac{\sin \mathrm{T}}{\mathrm{t}}& =& \frac{\sin \mathrm{R}}{\mathrm{r}}\\ \frac{\sin \left(19\right)}{9.5}& =& \frac{\sin \left(149\right)}{\mathrm{r}}\\ \mathrm{r}& =& \frac{\left(9.5\right)\times \sin \left(149\right)}{\sin \left(19\right)}\\ \mathrm{r}& =& \frac{9.5\times 0.7181}{0.2940}\\ \mathrm{r}& =& \frac{6.8219}{0.2940}\\ \mathrm{r}& =& 23.2039\mathrm{inches}\end{array}$

Hence, the the length of $r$ is equal to $23.20\mathrm{inches}$.