Question

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

Explanation:

Step1: Identify cosine relationship

In right $\triangle TSR$, $\cos(R) = \frac{\text{adjacent side}}{\text{hypotenuse}} = \frac{RS}{TR}$

Step2: Substitute known values

$TR=\sqrt{79}$, $\angle R=59^\circ$, so:
$\cos(59^\circ) = \frac{RS}{\sqrt{79}}$
Rearrange to solve for $RS$:
$RS = \sqrt{79} \times \cos(59^\circ)$

Step3: Calculate numerical values

First, $\sqrt{79} \approx 8.888$, $\cos(59^\circ) \approx 0.5150$
Multiply: $RS \approx 8.888 \times 0.5150 \approx 4.577$

Step4: Round to nearest tenth

$RS \approx 4.6$

Answer:

$4.6$