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.

130 views

To find the hypotenuse of a 45-45-90 triangle, multiply the length of one leg by √2 (approximately 1.414). In such a triangle, the legs are congruent, so if each leg is 'a', the hypotenuse 'c' is given by the formula c = a√2. For instance, if each leg is 5 units, the hypotenuse will be 5√2 (around 7.07). This simple relationship stems from the properties of the 45-45-90 triangle.**

FAQs & Answers

  1. What is the formula for finding the hypotenuse in a 45-45-90 triangle? The formula to find the hypotenuse 'c' is c = a√2, where 'a' is the length of one leg.
  2. Why is the hypotenuse in a 45-45-90 triangle equal to the leg length times √2? This relationship comes from the properties of isosceles right triangles, where the legs are equal and form a right angle.
  3. Can you give an example of calculating the hypotenuse? Sure! If each leg of the triangle is 5 units, the hypotenuse is 5√2, which is approximately 7.07 units.

Watch More

For more insights into triangle properties and angle calculations, check out our videos on the Pythagorean theorem and 30-60-90 triangle relationships.

  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. 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.
  3. 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.
  4. 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.