By Ezmeralda Lee | Updated Aug 30, 2022
Jean‑Philippe WALLET / iStock / GettyImages
Carpentry relies on accurate angles—whether you’re cutting a bevel, laying out a roof slope, or aligning a foundation. While many think trigonometry is daunting, it’s a straightforward tool that saves time, money, and frustration. Below is a concise, step‑by‑step guide that turns any angle‑cutting task into a quick, reliable calculation.
When you know the adjacent length and the desired angle, use the tangent function. For example, with a 55° angle and a 100‑inch adjacent side:
tan 55° = opposite ÷ 100″ ⇒ opposite = 100″ × tan 55° ≈ 142″
Apply the Pythagorean theorem (a² + b² = c²). Using the 100‑inch adjacent side and the 142‑inch opposite side from the previous step:
c² = 100² + 142² = 10 000 + 20 164 = 30 164 ⇒ c ≈ 173.7″
Angles in a triangle sum to 180°. If you have a right angle (90°) and one measured angle (55°), the remaining angle is:
90° + 55° + x = 180° ⇒ x = 35°
Use a calculator for all angle and distance calculations. Accurate trigonometry prevents costly rework, speeds up site layout, and ensures structural integrity. Keep a running log of your measurements; reusing these notes can save time on future projects.
Trigonometry is invaluable for:
Relying on trial and error for angles is inefficient and risky. The formulas above apply to any right‑angled scenario. For non‑right triangles, split the shape into two right triangles, compute each half, then recombine for the full solution.
