← Geometry and Trigonometry
Triangles, Angles & Right-Triangle Trigonometry
Angle relationships (parallel lines, triangle angle sum), the Pythagorean theorem, and SOH-CAH-TOA make up most SAT geometry/trig questions.
Core facts to have ready
A triangle's interior angles always sum to 180°. When a transversal crosses two parallel lines, corresponding angles are equal and co-interior (same-side interior) angles sum to 180°.
Pythagorean theorem: a² + b² = c² for a right triangle with legs a, b and hypotenuse c. SOH-CAH-TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
Worked Example
A right triangle has legs 6 and 8. Find the hypotenuse and sin(θ) for the angle opposite the side of length 6.
- Pythagorean theorem: 6² + 8² = c² → 36+64=100 → c=10.
- sin(θ) = opposite/hypotenuse = 6/10 = 3/5.
Answer: Hypotenuse = 10; sin(θ) = 3/5.
Key terms (1)
- SOH-CAH-TOA
- sin=opp/hyp, cos=adj/hyp, tan=opp/adj — the three basic right-triangle trig ratios.
Practice Quiz
Question 1 of 2Score so far: 0/0
A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?