What Is the Formula for a 90-Degree Triangle? Pythagorean Theorem Explained

Learn the formulas for solving 90-degree triangles, including the Pythagorean theorem and special angle triangles (45°-45°, 30°-60°).

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To solve for sides of a 90-degree triangle, use the Pythagorean theorem: a² + b² = c², where c is the hypotenuse, and a and b are the other two sides. For common angles like 45°-45° or 30°-60°, use special formulas: for a 45°-45° triangle, a = b and c = a√2; for a 30°-60° triangle, if a is opposite the 30° angle, b = a√3, and c = 2a.

FAQs & Answers

  1. What is the Pythagorean theorem? The Pythagorean theorem states that in a right triangle, the sum of the squares of the two legs (a and b) equals the square of the hypotenuse (c), expressed as a² + b² = c².
  2. How do you find the sides of a 45°-45°-90° triangle? In a 45°-45°-90° triangle, the legs are equal in length, and the hypotenuse is the leg length multiplied by the square root of 2.
  3. What are the side ratios in a 30°-60°-90° triangle? In a 30°-60°-90° triangle, the side opposite 30° is 'a', the side opposite 60° is 'a√3', and the hypotenuse is '2a'.