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.
Pythagoras Theorem Calculator
Why should you know the 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 the Pythagorean Theorem
- 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.
- 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.
- 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.
- 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.
- Electronics: The theorem is used to calculate the impedance of a circuit component, which is a measure of its resistance to electrical current.
- 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 Pythagorean 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 have been 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 popularised it.
Calculate 3 kinds of triangle
Using this Pythagoras theorem-based calculator, you can compute the area of the following types of triangle: While triangles have their own area formulas, you might also find our circle area calculator online helpful for computing circular measurements in geometric problems.
Area of a Right-Angled Triangle
A right-angled triangle has one angle at 90°, and the other two acute angles sum 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 the 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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