Question

the law of cosines for △rst can be set up as (s^{2}=7^{2}+3^{2}-2(7)(3)cos(s)). what could be true about △rst?
law of cosines: (a^{2}=b^{2}+c^{2}-2bccos(a))
(r = 5) and (t = 7)
(r = 3) and (t = 3)
(s = 7) and (t = 5)
(s = 5) and (t = 3)

Explanation:

Step1: Recall law of cosines formula

The law of cosines is $a^{2}=b^{2}+c^{2}-2bc\cos(A)$. In the given equation $s^{2}=7^{2}+3^{2}-2(7)(3)\cos(S)$, comparing with the law - of - cosines formula, we can see that $b = 7$, $c = 3$ and the side opposite to angle $S$ is $s$.

Answer:

D. $s = 5$ and $t = 3$ (assuming the sides of the triangle are named $r$, $s$, $t$ and the given equation is set up correctly with respect to the naming convention, and among the options, this is the one that aligns with the structure of the law - of - cosines application where the right - hand side has values related to two sides and the included - angle. Although the value of $s$ should be $\sqrt{7^{2}+3^{2}-2(7)(3)\cos(S)}$, from the perspective of side identification in the formula setup, this option is the most appropriate).