What Are the Formulas for Special Right Triangles (45-45-90 & 30-60-90)?

Learn the formulas for 45-45-90 and 30-60-90 special right triangles to quickly find side lengths without complex trigonometry.

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The formulas for special right triangles are: 45°-45°-90° triangle: Legs are equal; hypotenuse = leg × √2. 30°-60°-90° triangle: Hypotenuse = 2 × shorter leg; longer leg = shorter leg × √3. These relationships help easily calculate side lengths in these specific triangles without extensive trigonometry.

FAQs & Answers

  1. What is the side length relationship in a 45-45-90 triangle? In a 45-45-90 triangle, both legs are equal, and the hypotenuse is the leg length multiplied by the square root of 2.
  2. How do you find side lengths in a 30-60-90 triangle? In a 30-60-90 triangle, the hypotenuse is twice the length of the shorter leg, and the longer leg is the shorter leg multiplied by the square root of 3.
  3. Why are special right triangle formulas useful? These formulas allow quick calculation of side lengths without using complex trigonometry, saving time in geometry problems.

Watch More

For more insights into triangle properties and geometry shortcuts, explore our tutorials on the Pythagorean theorem, trigonometric ratios, and other special triangles to enhance your math skills.

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