Question

the law of cosines for △rst can be set up as 5² = 7² + 3² - 2(7)(3)cos(s). what could be true about △rst? law of cosines: a² = b² + c² - 2bccos(a) o r = 5 and t = 7 o r = 3 and t = 3 o s = 7 and t = 5 o s = 5 and t = 3

Explanation:

Step1: Recall law of cosines formula

The law of cosines is $a^{2}=b^{2}+c^{2}-2bc\cos(A)$, where $a$ is the side opposite angle $A$, and $b$ and $c$ are the other two - sides. In $\triangle RST$, if we compare $5^{2}=7^{2}+3^{2}-2(7)(3)\cos(S)$ with the law - of - cosines formula $a^{2}=b^{2}+c^{2}-2bc\cos(A)$, the side opposite angle $S$ is $s$, and the other two sides are $r$ and $t$. So $s = 5$, and the other two sides can be $r = 7$ and $t = 3$ or vice - versa.

Answer:

D. $s = 5$ and $t = 3$