Question

in $\triangle rst$, $overline{rs}=15$, $overline{rt}=12$, and $overline{st}=17$. which angle of $\triangle rst$ has the smallest measure?
a. $angle t$
b. $angle r$
c. cannot be determined
d. $angle s$

Explanation:

Step1: Recall triangle side-angle relationship

In any triangle, the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side.

Step2: Match sides to opposite angles

• Side $\overline{RS}=15$ is opposite $\angle T$
• Side $\overline{RT}=12$ is opposite $\angle S$
• Side $\overline{ST}=17$ is opposite $\angle R$

Step3: Identify shortest side and its angle

The shortest side is $\overline{RT}=12$, which is opposite $\angle S$.

Answer:

D. $\angle S$