Question

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

Explanation:

Step1: Match to law of cosines

Given law of cosines: $a^2 = b^2 + c^2 - 2bc\cos(A)$, where $a$ is the side opposite $\angle A$, and $b,c$ are the other two sides.
The given equation: $5^2 = 7^2 + 3^2 - 2(7)(3)\cos(S)$

Step2: Identify side-angle pairs

Here, $a=5$ (opposite $\angle S$), so side $s=5$ (side opposite $\angle S$ is labeled $s$). The other two sides are $7$ and $3$, which correspond to $r=7$ and $t=3$ (or vice versa; we check options).

Step3: Match with options

Check which option has $s=5$ and one of the other sides as 3.

Answer:

s = 5 and t = 3