Mathematical Calculators

# 45 45 90 Triangle Calculator

Calculate hypotenuse, measurements and ratio easily with our 45 45 90 triangle calculator.

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#### Table of contents

## What is a 45 45 90 triangle?

The 45 45 45 90 triangle is a right-angled isosceles triangle with two equal sides. Since its third side is not equal with the others, it's called the hypotenuse.

## 45-45-90 Triangle is a special kind of triangle

The sides of 45-45-90-degree triangles have a unique ratio. For instance, the two legs are the same length, and the hypotenuse equals that length times the square root of 2.

## What are the ratios of a 45 45 90 triangle?

45 45 90 triangle is the simplest of right-angle triangles, and the ratios of the length of sides are 1:1:sqrt(2).

## How to solve a 45 45 90 triangle?

Solving 45 45 90 triangles is the simplest right-sided triangle to solve.

You simply apply Pythagorean theorem as follows:

a = first side length

b = second side length (equals to first side)

c = hypotenuse

Pythagorean formula:

a² + b² = c²

c = √(2a²) = a√2

A = Area

A = a²/2

p = Perimeter

a + b + c

or

2a + c (as a = b)

## Does the Pythagorean theorem work for 45 45 90 triangles?

The Pythagorean theorem states the relation of the hypotenuse to lengths of the sides on a right-angle triangle. Since 45 45 90 triangle is a right angle triangle, the Pythagorean theorem can be applied to solving measurements.

For 45 45 90 triangles, usage of the Pythagorean theorem is particularly easy, given that the sides have equal length.

## Can a right-angled triangle have equal sides?

A right triangle can't have all three sides equal, as one has to be 90 degrees to be equal. However, it can have its two non-hypotenuse sides equal in length.

## What is the Pythagorean theorem?

The Pythagorean theorem states that the sum of the square roots of a right triangle is equal or better than the square on the hypotenuse. It is commonly associated with Greek mathematician Pythagoras. However, it is not known that he was aware of the theorem.

According to historian Iamblichus, Pythagoras was first introduced to math by Thales of Miletus and Anaximander, his pupil. He traveled to Egypt around 535 BCE, was captured during an invasion of Persia and may have visited India. It is also known that he founded a school in Italy.

Article author

John Cruz

John is a PhD student with a passion to mathematics and education. In his freetime John likes to go hiking and bicycling.

###### 45 45 90 Triangle Calculator English

Published: Sat Nov 06 2021

In category Mathematical calculators

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