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=(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.