use the information given in the figure to find the length st. if applicable, round your answer to the…

Explanation:

Step1: Apply the Pythagorean theorem in $\triangle RUT$

In right - triangle $\triangle RUT$, by the Pythagorean theorem $RU^{2}=RT^{2}-TU^{2}$. Given $RT = 13$ and $TU = 5$, then $RU=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}=12$.

Step2: Apply the Pythagorean theorem in $\triangle RUS$

In right - triangle $\triangle RUS$, $RS = 37$ and $RU = 12$. Let $SU=x$, then by the Pythagorean theorem $x=\sqrt{37^{2}-12^{2}}=\sqrt{(37 + 12)(37 - 12)}=\sqrt{49\times25}=\sqrt{49}\times\sqrt{25}=35$.

Step3: Calculate the length of $ST$

Since $SU=x$ and $TU = 5$, and $ST=SU - TU$, then $ST=35 - 5=30$.

Answer:

30