Right triangles and trigonometry
Use the right triangle tool first: Pythagorean theorem, special-triangle ratios, or SOH-CAH-TOA.
核心知识
Right triangles connect geometry to trigonometry. The Pythagorean theorem finds missing sides, special triangles give instant ratios, and SOH-CAH-TOA links angles to side lengths.
深入理解
Rule: Use the simplest right-triangle tool that fits the information you have.
- Two sides? Use the Pythagorean theorem.
- Special angles? Use 30-60-90 or 45-45-90 ratios.
- One angle and one side? Use sine, cosine, or tangent.
The hypotenuse is always the longest side, and complementary angles connect sine with cosine.
知识点教程
5Apply the Pythagorean theorem to find missing side lengths.
Use a^2 + b^2 = c^2 to find a missing side in any right triangle.
Use properties of special right triangles (30–60–90, 45–45–90).
Use 45-45-90 and 30-60-90 ratios to get exact side lengths fast.
Use right triangle trigonometry (sin, cos, tan) to solve for sides/angles.
Match the angle first, then choose sine, cosine, or tangent from the side ratio.
Use relationships between sine and cosine of complementary angles (SAT).
When sine and cosine are set equal, the two angles should add to 90 degrees.
Use similarity to compute trigonometric ratios when appropriate (SAT).
Similar right triangles keep the same trig ratios, so you can transfer a ratio from one copy to anot