Question

find rs.
write your answer as an integer or as a decimal rounded to the nearest tenth.
rs =

Explanation:

Step1: Use sine function

In right - triangle \(QRS\), \(\sin S=\frac{QR}{RS}\).

Step2: Substitute values

Given \(QR = 8\) and \(S=58^{\circ}\), so \(\sin58^{\circ}=\frac{8}{RS}\).

Step3: Solve for \(RS\)

\(RS=\frac{8}{\sin58^{\circ}}\). Since \(\sin58^{\circ}\approx0.848\), then \(RS=\frac{8}{0.848}\approx9.5\).

Answer:

$9.5$