Math, Geometry and Trigonometry, Stage 3
Right triangles and trigonometry on the SAT
In a right triangle, a² + b² = c², with c the hypotenuse. From an acute angle: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent (SOH-CAH-TOA). For complementary angles, sin(x) = cos(90° − x). π radians = 180°.
Loading practice…
| Triangle | Sides |
|---|---|
| 45°-45°-90° | s, s, s√2 |
| 30°-60°-90° | x, x√3, 2x |
| Common triples | 3-4-5, 5-12-13, 8-15-17, 7-24-25 |
Label the sides O, A and H from the angle named in the question before choosing a ratio.
Common mistakes
Adding legs for the hypotenuse5 and 12 give 13, not 17.
Opposite vs adjacentOpposite is the side not touching the angle.
Special-triangle mix-upOpposite 60° is x√3; the hypotenuse is 2x.
Sample questions with answers
1. Legs 5 and 12. Hypotenuse?
- 17
- 13 (correct)
- 60
- 169
√(25 + 144) = 13.
2. Right angle at C, BC = 8, AC = 15, AB = 17. sin A?
- 15/17
- 8/17 (correct)
- 8/15
- 15/8
Opposite A is BC = 8; hypotenuse 17.
3. What is 60° in radians?
- π/6
- π/3 (correct)
- π/2
- 2π/3
60 × π/180 = π/3.
Frequently asked questions
Is trigonometry on the SAT?
Yes, mostly right-triangle trigonometry. Geometry and Trigonometry makes up about 15% of SAT Math, roughly 5 to 7 questions. A reference sheet with key formulas is available during the test.
What is SOH-CAH-TOA?
sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
Why does sin(x) equal cos(90° − x)?
In a right triangle, the side opposite one acute angle is adjacent to the other.