Digital SAT · Math
Right-Triangle Trigonometry on the Digital SAT: All Question Types
Right-Triangle Trigonometry covers the sine, cosine, and tangent ratios, the special right triangles, and converting between degrees and radians. Most questions come down to labeling a triangle's sides relative to an angle, opposite, adjacent, and hypotenuse, then applying SOHCAHTOA. The special 30-60-90 and 45-45-90 triangles have fixed side ratios worth knowing, since they turn some questions into a quick lookup. A useful fact is that the sine of an angle equals the cosine of its complement, which several questions test directly. This is a Geometry and Trigonometry skill. Degree-radian conversion rests on a single anchor, that 180 degrees equals pi radians, so scaling from there handles any conversion the test asks for.
College Board skill: Geometry and Trigonometry: Right triangles and trigonometry
How Right-Triangle Trigonometry is tested
- how often it appears
- ~2 per test how often it appears
- typical difficulty
- Medium to hard typical difficulty
- practice questions in our bank
- 307 practice questions in our bank
SOH-CAH-TOA
Label the sides relative to the angle (opposite, adjacent, hypotenuse) and choose sine, cosine, or tangent accordingly.
Frequency and difficulty come from this skill's questions across our assembled full-length Digital SAT forms; the practice count is how many drills of these types are in our bank.
3 question types in Right-Triangle Trigonometry
In a right triangle the two acute angles add to 90 degrees, and that makes sine and cosine trade places: the sine of an angle equals the cosine of its complement, and the other way around.
In a right triangle, the two legs squared add up to the hypotenuse squared: a squared plus b squared equals c squared.
In a right triangle, sine, cosine, and tangent compare pairs of sides against an angle, packaged as SOH-CAH-TOA: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, tangent is opposite over adjacent.
Common questions
What is SOHCAHTOA?
A memory aid for the ratios: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. Labeling the sides relative to the angle first makes applying it straightforward.
How do I convert between degrees and radians?
Anchor on 180 degrees equals pi radians. To go from degrees to radians multiply by pi over 180, and to reverse it multiply by 180 over pi. Everything scales from that one equivalence.
Why does sine of an angle equal cosine of its complement?
In a right triangle the two non-right angles are complementary, and one angle's opposite side is the other's adjacent side. So the sine of one equals the cosine of the other, a relationship the test asks about directly.
Practice Right-Triangle Trigonometry the way it is tested
Start with the free 16-question diagnostic, then drill any of these types with step-by-step reasoning.