How to Find Missing Side Lengths in a 30-60-90 Triangle Explained

Learn how to calculate missing side lengths in a 30-60-90 triangle using side ratios for faster problem solving.

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In a 30-60-90 triangle, the side lengths follow a specific ratio. If you know the length of the shortest side (opposite 30°), the second side (opposite 60°) is shortest side × √3, and the hypotenuse is shortest side × 2. If another side is known, reverse the calculations to find the others.

FAQs & Answers

  1. What is the side length ratio in a 30-60-90 triangle? In a 30-60-90 triangle, the sides opposite these angles are in the ratio 1 : √3 : 2, corresponding to the shortest side, the longer leg, and the hypotenuse.
  2. How do I find the hypotenuse if I know the shortest side length in a 30-60-90 triangle? Multiply the shortest side length (opposite 30°) by 2 to get the hypotenuse.
  3. Can I calculate the sides if I know the hypotenuse of a 30-60-90 triangle? Yes, divide the hypotenuse by 2 to find the shortest side, then multiply the shortest side by √3 to find the second side.

Watch More

For further practice on special right triangles, check out our videos on 45-45-90 triangles and the Pythagorean theorem. These related topics build a solid foundation for mastering trigonometry and geometry problems.

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