How to Find Side Lengths of a 45-45-90 Triangle: Step-by-Step Guide

Learn how to calculate the side lengths of a 45-45-90 triangle using the special properties of this right triangle.

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45-45-90 triangles are special right triangles where the legs are congruent. If one leg is of length 'a', then the hypotenuse will be `a√2`. To find the side lengths, simply identify the length of one leg and multiply by the square root of 2 for the hypotenuse.

FAQs & Answers

  1. What is the ratio of the sides in a 45-45-90 triangle? In a 45-45-90 triangle, the two legs are congruent and the hypotenuse is the leg length multiplied by the square root of 2, giving a side ratio of 1:1:√2.
  2. How do you calculate the hypotenuse in a 45-45-90 triangle? Multiply the length of one leg by the square root of 2 to find the hypotenuse.
  3. Why is a 45-45-90 triangle called a special right triangle? Because its side lengths follow a consistent ratio that simplifies calculations and appears frequently in geometry problems.

Watch More

For more insights into special triangles and right triangle problems, explore our tutorials on 30-60-90 triangles and the Pythagorean theorem to enhance your geometry skills.

  1. Understanding the 45-45-90 Triangle Formula Discover the formula for a 45-45-90 triangle and learn how to calculate its sides effectively.
  2. Calculating the Hypotenuse of a 45-45-90 Triangle: A Step-by-Step Guide Learn how to easily find the hypotenuse of a 45-45-90 triangle with our quick and clear guide.
  3. Mastering Special Right Triangles: 45-45-90 and 30-60-90 Explained Learn how to solve special right triangles: 45-45-90 and 30-60-90. Discover their unique ratios for finding missing sides.
  4. 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.
  5. Finding Missing Side Lengths of a 30-60-90 Triangle Explained Learn how to calculate the missing side lengths of a 30-60-90 triangle using easy ratios.
  6. Understanding the 30-60-90 Triangle Rule: Essential Geometry Tips Explore the unique side ratios of 30-60-90 triangles and simplify your geometric calculations with this quick guide.
  7. How to Calculate Missing Side of a 30-60-90 Triangle Learn how to find the missing side of a 30-60-90 triangle using simple ratios.
  8. How to Identify a 30-60-90 Triangle: Essential Tips Learn how to identify a 30-60-90 triangle using angle measurements and side length ratios.
  9. How to Find the Long Leg of a 30-60-90 Triangle: Step-by-Step Formula Learn how to calculate the long leg of a 30-60-90 triangle using the formula long leg = short leg × √3 with easy examples.
  10. How to Calculate the Missing Side of an Isosceles Triangle Using the Pythagorean Theorem Learn how to find the missing side of an isosceles triangle with our step-by-step guide using the Pythagorean theorem.
  11. Understanding the 3 4 5 Rule for Right Angle Triangles Learn how the 3 4 5 rule helps determine right angle triangles effectively.