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45 45 90 Triangle Calculator

45 45 90 triangle calculator is a dedicated tool to solve this special right triangle. Find out what are the sides, hypotenuse, area and perimeter of your shape and learn about 45 45 90 triangle formula, ratio and rules.


There are various unique triangles that you will come across in math, one of them being the 45 45 90 triangle. The vertices of a triangle are often used to describe the shape. A triangle's three points are often indicated by the letters a b c (short for "a b c"). In addition, the side lengths of a triangle and the internal angles of triangles are often used to characterize them.

For example, an "isosceles" triangle has its two sides equal and is classified as a 45 45 90 triangle. With 45 45 90 degrees as its side’s angles, the values you'll be dealing with from this triangle can easily be calculated by a 45 45 90 triangle calculator.

45 45 90 triangles: a step-by-step guide (Formula)

Formulas used in the 45 45 90 triangle calculations can be used to calculate angles, substituting them for measurements. A right triangle with an isosceles angle is also known as a 45 45 90 triangle. Pythagorean Theorem can be applied here to find the hypotenuse because it is a right triangle. By way of illustration and explanation below, let's take a look at an example of a right triangle with 45 45 90 degrees of angle as one of its components.                                                                       

The triangle in the image above has 45 45 90 angles. For our hypotenuse, we'll use the Pythagorean Theorem:





The triangle formula for 45 45 90 angles.

The formulas of this triangle are also known as 45ers because of the unique ratio of their sides. The sum of the length of the two legs’ square roots is equal to the hypotenuse. In the diagram of this triangle, the ratio is illustrated in numbers.

The hypotenuse length is a√. In unique triangles, the hypotenuse length has a unique relationship that can be discovered in 45 45 90 triangular configurations. When you multiply two sides of this triangle (a) by the radical square root and divide the results by two, you get the answer. This can be done easily by using the 45 45 90 triangle calculator. When the hypotenuse of a 45 45 90 triangle is written as a radical, it is the simplest form of hypotenuse length. When solving 45 45 90 degree triangles, the Pythagorean Theorem can be used to compute the answer with the help of our triangle calculator.


45-45-90 triangle attributes

These are some of the characteristics of this triangle:

  1. This triangle always has a right angle in it.
  2. Two angles of this triangle are 45-degree similar.
  3. The third side (hypotenuse) of this triangle is always longer and the two sides have the same length.

The longest side is known as the hypotenuse, while the other two sides of the triangle, which are equal in length, are called the legs. Because the hypotenuse is always on the "opposite" (90-degree) side of the right angle in a 45-45-90 triangle, this triangle’s legs will always be joined together.

One method to recall these laws is to bear in mind that the total sum of the angles of this triangle is 180° and to help you achieve the correct and accurate measurements of this triangle a 45 45 90 triangle calculator will be the best tool for you to use.


45 45 90 triangle: Trigonometric ratios used.

When it comes to trigonometric ratios, you're talking about specific measurements of the angles in a right triangle. Make sure to remember that a right triangle has three sides, two legs, and a hypotenuse. The tangent, the cosine, and the sine are the three major ratios in trigonometry.  An angle that isn't 90 degrees in a right triangle may be calculated by the use of tangent, cosine, or sine. Below are the trigonometric ratios used to calculate this triangle?

The sine and cosine functions “trigonometry study", can be applied in this triangle. Both are equal (1) because of the 45-degree angle and so this means that,

a/c= 1/√2 so c = a√2.

Use the simple triangular area formula to get the size of this triangle that is,

Area = 1/2 × base × height

So let us find the perimeter of the triangle,

Perimeter = a + b + c = a + a + a√2 = a (2+√2)


An example below of how to solve the 45 45 90 triangles

Using the diagram above, calculate the base length and the height if its hypotenuse is 6√2cm.


  • n: n: n2 is the triangle's ratio. So, here we are;
  • n√2=6√2cm
  • The equation must be squared on both sides:
  • (n√2) 2 = (6√2)2cm
  • 2n2=36×2
  • 2n2=72
  • n2=36