Question

find st.

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

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle $\triangle RTS$, right-angled at $T$. For angle $\angle S = 31^\circ$, side $RT = 3$ is the opposite side, and $ST$ is the adjacent side. We use the tangent ratio:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

Substitute $\theta = 31^\circ$, opposite $= 3$, adjacent $= ST$:
$\tan(31^\circ) = \frac{3}{ST}$

Step3: Solve for $ST$

Rearrange the equation to isolate $ST$:
$ST = \frac{3}{\tan(31^\circ)}$
Calculate $\tan(31^\circ) \approx 0.6009$, so:
$ST \approx \frac{3}{0.6009} \approx 5.0$

Answer:

$5.0$