This Pythagorean theorem calculator will calculate the length of any of the missing sides of a right triangle,area of a triangle be it isosceles triangle or equilateral triangle or, area of right angle triangle or the hypotenuse of the right triangle by using the hypotenuse formula.

## Why should you Know Pythagorean theorem ?

The Pythagorean Theorem has many practical applications, especially in the field of geometry. For example, it can be used to find the distance between two points on a coordinate plane, the length of a diagonal of a rectangle, or the height of a right triangle given its base and hypotenuse.

Here’s an example: Suppose you have a right triangle with legs of length 3 and 4 units. To find the length of the hypotenuse, you can use the Pythagorean Theorem.

a^2 + b^2 = c^2 3^2 + 4^2 = c^2 9 + 16 = c^2 25 = c^2

Taking the square root of both sides gives c = 5. Therefore, the length of the hypotenuse is 5 units.

## Practical Use of Pythagorean theorem

1. Construction: The theorem is commonly used by builders and architects to determine the length of diagonal braces needed to reinforce a rectangular structure like a roof or a wall.
2. Navigation: The Pythagorean Theorem is used in navigation to calculate distances between two points. For example, if you know the latitude and longitude of two points on a map, you can use the theorem to find the distance between them.
3. Surveying: Surveyors use the theorem to measure the distance between two points that cannot be directly measured, such as the height of a tall building or the depth of a well.
4. Physics: In physics, the theorem is used to calculate the magnitude of vectors, which are quantities that have both a direction and a magnitude. For example, the force of gravity acting on an object can be calculated using the theorem.
5. Electronics: The theorem is used to calculate the impedance of a circuit component, which is a measure of its resistance to electrical current.
6. Sports: The Pythagorean Theorem is used in sports to calculate the distance between the pitcher’s mound and home plate in baseball, and to calculate the distance between the three-point line and the basket in basketball.

## What is the Pythagorus theorem?

The Pythagoras theorem is if the sides of a right angle triangle are a and b and the hypotenuse is, the formula is ,

a2 + b2 = c2

This mathematical theorem is credited to be developed in the sixth century BC by the Greek philosopher and mathematician Pythagoras, . Note that this theory was found used by the Indians and Babylonians, Pythagoras (or his students) , much before Pythagoras who actually popularized it.

## Calculate 3 kinds of triangle

Using this Pythagoras theoram based calculator, you can compute area of following types of triangle:

### Area of a Right Angled Triangle

A right-angled triangle has one angle at 90° and the other two acute angles sums to 90°. Therefore, the height of the triangle will be the length of the perpendicular side. You can compute the area of a right angle triangle by using following formula

Area of a Right Triangle = A = ½ × Base × Height

### Area of an Equilateral Triangle

An equilateral triangle is one whose all the sides are equal. Calculate the area of the equilateral triangle using the following formula:

Area of an Equilateral Triangle = A = (√3)/4 × side2

### Area of an Isosceles Triangle

An isosceles triangle has two of its sides equal and also the angles opposite the equal sides are equal.

Area of an Isosceles Triangle = A = ½ (base × height)

`a² + b² = c²`

You can practice with our Pythagorean theorem calculator .

## Find Sides of Traingle Pythagorous Theorem

Using the Pythagoras theorem, you can find the length of an unknown side and the angle of a triangle. By this theorem, we can derive the base, perpendicular and hypotenuse formula. For example, suppose you want to find the hypotenuse (c) of a right-angled triangle with a base of 7 cm and a height of 8 cm.

Then , use Pythagoras theorem a2 + b2 = c2

c2=72 + 82

c2=49+64=113

c=113

c=√113= 10.6

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