In triangle $rst$, $r$ = $58$ cm, $\angle s$ = $48°$ and $\angle t$ = $29°$. Find the length of side $s$, to the nearest centimeter.

• A. $27$ cm
• B. $44$ cm
• C. $36$ cm
• D. $52$ cm

Answer: (B)

Verified step by step guidance

1. Identify the given elements in triangle \( rst \): side \( r = 58 \) cm, angle \( \angle s = 48^\circ \), and angle \( \angle t = 29^\circ \).
2. Calculate the remaining angle \( \angle r \) using the triangle angle sum property: \( \angle r = 180^\circ - \angle s - \angle t = 180^\circ - 48^\circ - 29^\circ \).
3. Use the Law of Sines, which states that \( \frac{r}{\sin(\angle r)} = \frac{s}{\sin(\angle s)} = \frac{t}{\sin(\angle t)} \), to set up a proportion to find side \( s \).
4. Rearrange the Law of Sines formula to solve for \( s \): \[ s = \frac{r \times \sin(\angle s)}{\sin(\angle r)} \].
5. Substitute the known values of \( r \), \( \angle s \), and \( \angle r \) into the formula and calculate \( s \), then round the result to the nearest centimeter.