Pythagorean Theorem & Right-Triangle Trig
Practice the key formulas, special triangles, and trig ratios for solving right triangles.
Keyboard Shortcuts
💡 Pro tip: Use keyboard shortcuts for faster studying!
Study Smart Tips for Pythagorean Theorem & Right-Triangle Trig
Master these concepts using proven study techniques that actually work:
Active Recall
Test yourself before flipping each card to strengthen memory retention
Spaced Repetition
Review difficult cards more frequently than easy ones
Multiple Sessions
Break study time into shorter, focused sessions
Explain Aloud
Verbalize answers to reinforce understanding
Questions Covered in This Set
10 cards to master
State the Pythagorean Theorem and define each variable.
a² + b² = c², where a and b are the legs (sides forming the right angle) and c is the hypotenuse (longest side, opposite the right angle).
A right triangle has legs 6 and 8. Find the hypotenuse.
36 + 64 = 100, so c = √100 = 10.
Hypotenuse = 13, one leg = 5. Find the other leg.
25 + b² = 169 → b² = 144 → b = 12.
List four common Pythagorean triples.
3-4-5, 5-12-13, 8-15-17, 7-24-25 (plus all multiples, like 6-8-10 and 30-40-50).
What does the converse of the Pythagorean Theorem tell you?
If a² + b² = c², the triangle is right; if a² + b² < c², it's obtuse; if a² + b² > c², it's acute.
Side relationships in a 45°-45°-90° triangle?
The two legs are equal; hypotenuse = leg × √2. (Leg 5 → hypotenuse 5√2 ≈ 7.07)
Side relationships in a 30°-60°-90° triangle?
Short leg = x (opposite 30°), long leg = x√3 (opposite 60°), hypotenuse = 2x.
What does SOH-CAH-TOA stand for?
sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj.
A ramp is 40 ft long and rises at 12°. How tall is it?
Height is opposite, hypotenuse known → sine: h = 40 sin12° ≈ 8.3 ft.
A tree is 18 m tall with a 30 m shadow. Find the sun's angle of elevation.
tan θ = 18/30 = 0.6 → θ = tan⁻¹(0.6) ≈ 31.0° (calculator in degree mode).
