Right-Triangle Trigonometry
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalThree ratios and one identity cover SAT trig. The points leak in the sides, an adjacent leg landing in a sine or the hypotenuse sneaking into a tangent, in the identity, sine-equals-cosine solved as an equality or sent through 180 instead of 90, and at the end, in the owner: the other acute angle's ratio, a flipped fraction, or a ratio's bare numerator reported as a side length.
These patterns aren't really about whether you memorized SOH-CAH-TOA. They're about whether opposite and adjacent got located from the angle actually named, whether equal sine and cosine sent the angles to a 90-degree sum, and whether the answer belongs to the angle and quantity the question asked about.
The work
4 ways in · any order
Lesson
Right-Triangle Trigonometry
›
Locate opposite and adjacent from the named angle before writing any fraction, send sine-equals-cosine through the complementary sum, scale ratios up to real side lengths, and re-seat before answering for the other angle. The lesson works the method and the three patterns that derail it, and it saves the trap for last: the right ratio for the wrong angle.
Diagnostic
10-item topic check
›
Ten items across the three patterns: ratios built from the wrong sides, the complementary identity missed or bent, and reciprocals or unscaled values reported. A mix of labeled triangles, ramps, cofunction equations, and ratio-to-side scaling. Take it cold to surface the ones still catching you, or after the lesson to confirm they are gone.
Grid-in Check
Student-produced response
›
About a quarter of SAT math answers are typed, not chosen, with no options to react to. These grid-in items diagnose by the value you enter, then route into the same drills the multiple-choice check feeds.
Targeted Practice
Drill a single pattern
›
Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the pattern and you move on.