Question

1. determine the length of rt to the nearest tenth of a metre.

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Explanation:

Step1: Identify the trigonometric relation

In right - triangle RST, we know the length of side RS = 25.0 m and angle R = 22°. We want to find the length of RT. Since cosine of an angle in a right - triangle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, and $\theta = 22^{\circ}$, the adjacent side to angle R is RT and the hypotenuse is RS. So, $\cos R=\frac{RT}{RS}$.

Step2: Solve for RT

We can re - arrange the formula $\cos R=\frac{RT}{RS}$ to get $RT = RS\times\cos R$. Substitute RS = 25.0 m and $R = 22^{\circ}$. We know that $\cos(22^{\circ})\approx0.9272$. Then $RT=25.0\times0.9272 = 23.2$ m.

Answer:

23.2 m