Curriculum fit: Digital SAT Math, Geometry and Trigonometry domain. Practice questions here are original, not official SAT questions. US: Geometry.
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What is it?
This domain covers area and volume, lines and angles, triangles, right-triangle trigonometry and circles. Many questions combine more than one idea, such as using similar triangles and the Pythagorean theorem together.
Draw a clear diagram, label what you know, and write the relevant formula before substituting numbers. Check the official College Board materials for the formulas provided during the test.
Key formulas and ideas
- Pythagorean theorem: a² + b² = c² in right triangles.
- Special right triangles: 45-45-90 sides are in the ratio 1 : 1 : √2; 30-60-90 sides are in the ratio 1 : √3 : 2.
- sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent.
- Circle with centre (h, k) and radius r: (x − h)² + (y − k)² = r².
- π radians = 180 degrees.
Worked examples
Pythagorean theorem
A right triangle has legs 5 and 12. Find the hypotenuse.
- c² = 5² + 12² = 25 + 144 = 169.
- c = 13.
✓ Answer 13
Equation of a circle
What are the centre and radius of (x − 3)² + (y + 2)² = 25?
- Compare with (x − h)² + (y − k)² = r².
- h = 3 and k = −2 (because y + 2 = y − (−2)).
- r² = 25, so r = 5.
✓ Answer Centre (3, −2), radius 5
Trigonometric ratio
In a right triangle with hypotenuse 5, sin θ = 3/5. Find cos θ.
- The opposite side is 3 and the hypotenuse is 5.
- The adjacent side is √(25 − 9) = 4.
- cos θ = adjacent ÷ hypotenuse = 4/5.
✓ Answer 4/5
Common mistakes to avoid
- Forgetting that the sign in (y + 2) means k = −2.
- Using the diameter as the radius.
- Mixing up sine and cosine.
- Not checking the units or whether the angle is in degrees or radians.
Practice questions
Frequently asked questions
Are formulas provided on the test?
College Board provides some reference information. Check its current official guidance and practise with it before test day.
How do I convert degrees to radians?
Multiply by π/180. For example, 90° = π/2 radians.
Keep going with these guides
Pythagoras' theorem: how to find a missing side
Use a² + b² = c² to find any side of a right-angled triangle. Worked examples for GCSE, and the Pythagorean theorem in US Geometry.
KS3GCSEMiddle SchoolHigh SchoolSOH CAH TOA: how to find sides and angles in a triangle
Use sine, cosine and tangent to find missing sides and angles in right-angled triangles, with step-by-step examples for GCSE and high school Geometry.
GCSEHigh SchoolCircle theorems explained: rules, examples and reasons
Learn the main circle theorems and use them to find angles with a reason for every step. GCSE Higher and high school Geometry, with worked examples.
GCSEA-LevelHigh SchoolSources and review
- College Board: The SAT Math section
- College Board: How the SAT is structured
- Common Core State Standards: Mathematics (high school)
Reviewed by StudyMorrow editorial review on 5 Nov 2026.