Understanding 30-60-90 and 45-45-90 Triangle Rules

Learn the key rules and ratios of 30-60-90 and 45-45-90 triangles for solving geometric problems.

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For a 30-60-90 triangle, the side ratios are always 1 : √3 : 2. The shortest side is opposite the 30° angle, the length of the side opposite the 60° angle is √3 times the shortest side, and the hypotenuse is twice the shortest side. For a 45-45-90 triangle, the ratios are 1 : 1 : √2. Both legs are of equal length, and the hypotenuse is √2 times a leg. These rules help in solving many geometric problems efficiently.

FAQs & Answers

  1. What is the ratio of sides in a 30-60-90 triangle? The side ratios for a 30-60-90 triangle are 1 : √3 : 2.
  2. How do you find the hypotenuse of a 45-45-90 triangle? The hypotenuse of a 45-45-90 triangle is √2 times the length of one leg.
  3. What is a practical application of 30-60-90 triangles? 30-60-90 triangles are often used in construction and design for creating precise angles.
  4. How do I remember the rules for 45-45-90 and 30-60-90 triangles? You can remember the 45-45-90 triangle has equal legs and a hypotenuse of √2 times a leg, while the 30-60-90 triangle side lengths follow the 1 : √3 : 2 ratio.

Watch More

If you found this explanation of triangle rules helpful, check out our other videos on geometry concepts, including area calculations and the Pythagorean theorem.

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