Question

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

Explanation:

Step1: Identify cosine relationship

In right $\triangle RST$, $\cos(\angle T) = \frac{ST}{TR}$

Step2: Substitute known values

$\angle T=24^\circ$, $TR=\sqrt{45} \approx 6.708$, so:
$\cos(24^\circ) = \frac{ST}{\sqrt{45}}$

Step3: Solve for ST

Rearrange to isolate ST:
$ST = \sqrt{45} \times \cos(24^\circ)$
Calculate $\cos(24^\circ) \approx 0.9135$, so:
$ST \approx 6.708 \times 0.9135 \approx 6.1$

Answer:

$6.1$