Understanding the Side Ratio of a 45-45-90 Triangle | Explained with Math Formula and Example

The side ratio of a 45-45-90 triangle is …

The side ratio of a 45-45-90 triangle is 1:1:√2

The side ratio of a 45-45-90 triangle is 1:1:√2.

A 45-45-90 triangle is a special type of right triangle where the two acute angles are both equal to 45 degrees. This means that the remaining angle, the right angle, is 90 degrees.

Since the sum of the angles in any triangle is always 180 degrees, the two 45 degree angles together add up to 90 degrees. This is why this triangle is called a 45-45-90 triangle.

In a 45-45-90 triangle, the lengths of the sides have a specific ratio. The two legs (the sides opposite to the 45 degree angles) are equal in length, and the hypotenuse (the side opposite to the right angle) is equal to the length of a leg times the square root of 2 (√2).

So, if we let the length of each leg be “x,” then the length of the hypotenuse will be x√2.

Therefore, the side ratio of a 45-45-90 triangle is 1:1:√2, meaning that the lengths of the sides are in the ratio of 1, 1, and √2.

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