In these lessons, we will learn
A 45-45-90 triangle is a special right triangle whose angles are 45°, 45° and 90°.
The lengths of the sides of a 45-45-90 triangle are in the ratio of
The following diagram shows a 45-45-90 triangle and the ratio of its sides. Scroll down the page for more examples and solutions using the 45-45-90 triangle.
Note that a 45-45-90 triangle is an isosceles right triangle. It is also sometimes called a 45-45 right triangle.
A right triangle with two sides of equal lengths is a 45-45-90 triangle.
You can also recognize a 45-45-90 triangle by the angles. As long as you know that one of the angles in the right-angle triangle is 45° then it must be a 45-45-90 special right triangle.
A right triangle with a 45° angle must be a 45-45-90 special right triangle.
Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are both 3 inches.
Step 1: This is a right triangle with two equal sides so it must be a 45-45-90 triangle.
Step 2: You are given that the both the sides are 3. If the first and second value of the ratio n:n:n√2 is 3 then the length of the third side is 3√2
Answer: The length of the hypotenuse is 3√2 inches.
Find the lengths of the other two sides of a right triangle if the length of the hypotenuse is 4√2 inches and one of the angles is 45°.
Step 1: This is a right triangle with a 45° so it must be a 45-45-90 triangle.
Step 2: You are given that the hypotenuse is 4√2. If the third value of the ratio n:n:n√2 is 4√2 then the lengths of the other two sides must 4.
Answer: The lengths of the two sides are both 4 inches.
The following videos show more examples of 45-45-90 triangles.How to find the length of a leg or hypotenuse in a 45-45-90 triangle using the Pythagorean Theorem and then derive the ratio between the length of a leg and the hypotenuse?
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.