SAT and ACT math terms · SAT Math, ACT Math
Right-triangle trigonometry (SOH-CAH-TOA)
Also called: SOH-CAH-TOA
Right-triangle trigonometry (SOH-CAH-TOA): The ratios sine, cosine and tangent relate a right triangle's acute angles to its side lengths.
By the CollegePrepRoom editorial team · Updated · How we write and check these pages
What it means
sin θ = opposite / hypotenuse, cos θ = adjacent / hypotenuse, tan θ = opposite / adjacent. A useful identity: for complementary angles, sin x° = cos(90 − x)°.
Trig ratios depend only on the angle, because similar triangles have equal side ratios.
Example
In a right triangle with legs 6 and 8 and hypotenuse 10, the sine of the angle opposite the side of length 6 is 6/10 = 0.6.
On the exam
The SAT tests trig ratios and the complementary-angle relationship; the ACT also tests the unit circle and trigonometric graphs.
Lessons and practice questions
Related terms
- Pythagorean theoremIn a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: a² + b² = c².
- RadianA unit of angle measure where one radian is the angle that cuts off an arc equal in length to the radius; 2π radians equal 360°.
- Similar trianglesTriangles with the same shape: corresponding angles are equal and corresponding sides are proportional.