# Hypotenuse Calculator

With this hypotenuse calculator you will quickly find this longest side of a right triangle.

two sides ∟  cm
cm
Hypotenuse
cm

Our hypotenuse calculator makes it simple for you to calculate our right-angled triangle hypotenuse’. This calculator software will appeal to you since it is capable of doing mathematical operations when it comes to calculating the hypotenuse of a right triangle. Please don't hesitate to utilize this hypotenuse calculator right now!

## Defining the hypotenuse of a right triangle

In all right-angled triangles, the hypotenuse is always the longest side. The left side refers to the opposite side of a right angle (90°).

## Right angle triangle hypotenuse

With the many formulae built in it, this hypotenuse calculator ensures that it works in various situations when calculating angles in a right-angle triangle. Right angle triangle hypotenuses are longer due to their placement opposite the 900 angle, making them longer than the other two sides. The Pythagorean Theorem may also be used to demonstrate this, which states that:

a2 b2=c2

a² > b², a² > c²

a > b, a > c

As you can see, the hypotenuse (a) is longer than the other two sides (base and height) as an outcome of the method explained above.

## Finding the triangle's hypotenuse using the hypotenuse calculator

The hypotenuse of a triangle can be calculated in three different ways,

1. Calculating the angle and one leg using this formula, c = a / sin (α) = b / sin (β)

sin⁡A/a = sin⁡B/b = sin⁡C/c

2. The two legs of all right triangles use the Pythagorean Theorem to calculate this formula. (c = √ (a² + b²) or c² = a² + b²)

3. Calculating the area and one leg using this formula (c = √ (a² + b²) = √ (a² + (area _ 2 / a)²) = √((area _ 2 / b)² + b²). This calculation is based on the formula we use to determine the area of a triangle (1/2 × b × h). It follows the same reasoning as the other two approaches of determining hypotenuses. This hypotenuse calculator may be used to calculate all the formulas above.

## Solving a hypotenuse equation using a hypotenuse calculator

### Equation of the Hypotenuse

The hypotenuse formula is as follows: A triangle with a right angle or a 90° angle may be used to frame squares since each of the triangle's three sides can be used. As soon as the squares are placed on each side, it is discovered that each square has the same area. The finding is eventually summarized in a hypotenuse equation, which may also be referred to as a short equation.

The total sum of the other two sides’ lengths of a right-angled triangle is equal to the hypotenuse equation.

a2 + b2 =c2.

Now, look at the diagram shown below which explains clearly how this formula was derived. We have a = Perpendicular, b = Base, c = Hypotenuse in this diagram.

### Hypotenuse Tips & Tricks:

The hypotenuse and its relationship to the other two sides of the right triangle may be understood clearly by taking into consideration the information below,

If Pythagoras' theorem is applied in any right-angled triangle,

• The longest side of a right triangle which is the hypotenuse equals the total sum of the squares of the base and height thus, Hypotenuse2 = Base2 + Perpendicular2 and is the mathematical representation for this.
• Equation for the hypotenuse is: a2 + b2= c2. The right triangle's a, b, and c form the hypotenuse.
• The hypotenuse leg theorem argues that if the hypotenuse and leg sides are equal, then the two triangles are congruent. Determining the hypotenuse of a right-angled triangle will never be a problem for you again. Solving right-angled equations will be simple with our hypotenuse calculator. To do so, you need to know the triangle’s base and perpendicular values.

Hypotenuse2 = Base2 + Perpendicular2 may be used to get the length of the hypotenuse in a right triangle with a base length of 3ft and a perpendicular length of 4ft. Hypotenuse2 = 32 + 42 = 9 + 16 = 25 is obtained by replacing the values of the base and perpendicular. This means that the hypotenuse is 5ft long in that triangle. This is how the hypotenuse equation may be used to quickly determine the hypotenuse's length with the help of our hypotenuse calculator.

To determine the hypotenuse of a triangle, let's analyze one more example. One side of the right triangle has a length of 8ft, while the opposing side measures 6ft, and the base has a length of 8ft.

(Hypotenuse) 2 = (Base) 2 + (Perpendicular) 2 = 62 + 82 = 36 + 64 = 100. So Hypotenuse = √100 = 10ft.

With the same equation, the perpendicular side of the hypotenuse's base may be quickly and readily determined for any given value using the hypotenuse calculator.

### Hypotenuse theorem

The Pythagorean Theorem may be used to connect the base and height of a right-angled triangle to the hypotenuse. A triangle's hypotenuse2 is equal to the sum of its base2 and its height2, according to the Pythagorean Theorem. A right triangle's hypotenuse is known as the longest side of a right-angled triangle, this means that hypotenuse2 is equal to the sum of the hypotenuse and the height and the base. In mathematics, this is called the hypotenuse rule. Together, the hypotenuse, height, and triangular base lengths make up the Pythagorean triplets, for instance (25, 24, 7).

## Summary

By using the hypotenuse calculator, you can figure out what the hypotenuse of a right-angled triangle is by entering the angle at which the triangle is formed in the calculator. A right triangle's hypotenuse may be calculated with this tool. To make use of the hypotenuse calculator, enter the values into the appropriate input boxes shown in the calculator.