Question

find st.
s
t
54°
5
r
write your answer as an integer or as a decimal rounded to the nearest tenth.
st =
submit

Explanation:

Step1: Identify adjacent side, angle

We know $\angle T = 54^\circ$, adjacent side $RT = 5$, and $ST$ is the hypotenuse.

Step2: Use cosine definition

Cosine of angle is adjacent over hypotenuse.
$\cos(54^\circ) = \frac{RT}{ST}$

Step3: Rearrange to solve for ST

Isolate $ST$ by rearranging the formula.
$ST = \frac{RT}{\cos(54^\circ)}$

Step4: Substitute values and calculate

Plug in $RT=5$ and $\cos(54^\circ)\approx0.5878$.
$ST = \frac{5}{0.5878} \approx 8.5$

Answer:

$8.5$