If you recall SOHCAHTOA and your trig/inverse trig relationships… The fact that s / t is equal to tan(0.697) and all those other trig values may seem completely abstract, but there’s actually an easy way to conceptualize it. The only other information that’s given is that the ratio of the two sides, s / t, is equal to some angles plugged into some trigonometric functions. It’s clear that the question is asking us to find the measure of the angle β (Beta), but the method we’re supposed to use isn’t readily apparent. Let’s try and break it down, though, to get a better understanding of what we’re working with here. At first glance, you may have no idea how to solve it. Looks pretty difficult, right? I took this problem straight from Khan Academy’s SAT prep questions. Given that s / t ≈ tan(0.697) ≈ sin(0.994) ≈ cos(0.576), approximately what is the measure of angle β in radians, to the nearest tenth?” The question reads: “Side length t is 6.43 and s is 5.39. (Note: If you think you’ve already got a good understanding of trigonometry and just want to see the solution, you can skip ahead to “Solving the Problem.”) Let’s take a look at the problem that this student was struggling with. Because of their relatively high difficulty compared to other questions, I felt it was appropriate to address an example of how I’d go about solving one in a blog post. In my opinion, these are some of the hardest questions that the SAT tests you on.

More specifically, they were struggling with Right Triangle Trigonometry questions. Recently, I’ve been tutoring for the SAT, and I noticed one of my students was struggling with some of the SAT math questions.

Sat trig cheat sheet