Question

In ΔRST, s = 93 inches, ∠S=123° and ∠T=28°. Find the length of r, to the nearest 10th of an inch.

Answer 1

We have been given that in ΔRST, s = 93 inches, ∠S=123° and ∠T=28°. We are asked to find the length of r to the nearest 10th of an inch.

We will use law of sines to solve for side r.

$\frac{a}{\text{Sin}(a)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}$, where a, b and c are corresponding sides to angles A, B and C respectively.

Let us find measure of angle S using angle sum property of triangles.

$\angle R+\angle S+\angle T=180^{\circ}$

$\angle R+123^{\circ}+28^{\circ}=180^{\circ}$

$\angle R+151^{\circ}=180^{\circ}$

$\angle R+151^{\circ}-151^{\circ}=180^{\circ}-151^{\circ}$

$\angle R=29^{\circ}$

$\frac{r}{\text{sin}(R)}=\frac{s}{\text{sin}(S)}$

$\frac{r}{\text{sin}(29^{\circ})}=\frac{93}{\text{sin}(123^{\circ})}$

$\frac{r}{\text{sin}(29^{\circ})}\cdot \text{sin}(29^{\circ})=\frac{93}{\text{sin}(123^{\circ})}\cdot \text{sin}(29^{\circ})$

$r=\frac{93}{0.838670567945}\cdot (0.484809620246)$

$r=110.889786233799179\cdot (0.484809620246)$

$r=53.7604351$

Upon rounding to nearest tenth, we will get:

$r\approx 53.8$

Therefore, the length of r is approximately 53.8 inches.