Question

find st.

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

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle $\triangle SUT$, right-angled at $S$. We know $\angle U = 67^\circ$, hypotenuse $UT = 6.5$, and we need to find $ST$ (the side opposite $\angle U$). We use the sine function:
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

Substitute $\theta = 67^\circ$, hypotenuse $=6.5$, opposite $=ST$:
$\sin(67^\circ) = \frac{ST}{6.5}$

Step3: Solve for $ST$

Rearrange to isolate $ST$:
$ST = 6.5 \times \sin(67^\circ)$
Calculate $\sin(67^\circ) \approx 0.9205$, so:
$ST \approx 6.5 \times 0.9205$

Step4: Compute final value

$ST \approx 6.0$

Answer:

$6.0$