Definition
Exact triangle ratios are side ratios from special right triangles used to compute trig values without decimals.
Why It Matters
These ratios are the “DNA” of special right triangles, providing the exact values that anchor the unit circle and coordinate geometry. Memorizing these instead of decimals ensures that your geometric reasoning remains structurally sound, preventing the “rounding rot” that can compromise high-stakes calculations.
Core Concepts
- They produce values such as , , and .
- How to read: “The values are one-half, the square root of two all over two, and the square root of three all over two.”
- Meaning: Exact side ratios from 30-60-90 and 45-45-90 triangles—memorize these instead of decimal approximations.
- This concept is part of the chapter-by-chapter synthesis from Trigonometry For Dummies.
- It should be merged with existing math notes if a stronger canonical note already exists.