Question

1. determine the length of side r to the nearest tenth of a metre. short answer

Explanation:

Step1: Identify the trig - ratio

In right - triangle \(RST\) with right - angle at \(S\), we know the adjacent side to angle \(R\) (\(RS = 21.1\) m) and we want to find the opposite side (\(r=ST\)). We use the tangent function since \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), where \(\theta = 26^{\circ}\).
\(\tan R=\frac{r}{RS}\)

Step2: Substitute the values

We know that \(R = 26^{\circ}\) and \(RS = 21.1\) m. Substituting into the formula \(\tan R=\frac{r}{RS}\), we get \(\tan(26^{\circ})=\frac{r}{21.1}\).
Since \(\tan(26^{\circ})\approx0.4877\), the equation becomes \(0.4877=\frac{r}{21.1}\).

Step3: Solve for \(r\)

Multiply both sides of the equation by \(21.1\): \(r = 21.1\times\tan(26^{\circ})\).
\(r=21.1\times0.4877\approx10.3\) m.

Answer:

\(10.3\) m