Triangle $ABC$ is similar to triangle $XYZ$, where angle $A$ corresponds to angle $X$ and angles $C$ and $Z$ are right angles. If $cot(Y) = √111/17$, what is the value of cot($B$)?
The correct answer is (A).
current priority level - the Path to 550+ and higher
The reason why this question does not have a current priority level of we all want this one is because we do love it when any student of ours embraces her or his preferences and trig just is not one of them. That said, if you’re reading this, and you do not love trig, you’ll end up agreeing that loving trig or not ends up being a non-factor. Vamos.
This is another question that we would deem to be “trig”, as no actual trig knowledge is required here. So, if you do not have SohCahToa at your fingertips, you’re good still here. If you don’t remember what cot is, you’re good still here.
We can smoothly arrive at (A) as our correct answer by acknowledging that since angle $A$ corresponds to angle $X$ and angles $C$ and $Z$ are the same, it would mean that angle $B$ corresponds to angle $Y$. Therefore, no matter which trig function is mentioned, whatever would be the case for angle $Y$ will also be the case for angle $B$.
We definitely could put forth that this is really a geometry question testing us on our understanding of similar triangles. We might even be able to put forth that this isn’t even a geometry question, as even if we knew nothing about similar triangles, given how this question is worded, we could have thought that cot($Y$) and cot($B$) are the same.
To close out, if you are on a Path to 600+…