Hypotenuse Calculator is a free online tool that helps to find the hypotenuse of a right-angled triangle. The hypotenuse is the longest side of a right triangle. Furthermore, it is the side opposite the right angle. Show
What is a Hypotenuse Calculator?Hypotenuse Calculator helps to calculate the hypotenuse of a right triangle with a given base and height. The Pythagoras Theorem is used to calculate the hypotenuse of a right triangle. To use the hypotenuse calculator, enter the values in the given input boxes. Hypotenuse CalculatorNOTE: Enter values upto 3 digits only. How to Use the Hypotenuse Calculator?Follow the steps given below to find the hypotenuse of a right triangle using the hypotenuse calculator:
How Does Hypotenuse Calculator Work?A triangle in which one angle measures 90 degrees and the remaining two angles are acute is known as a right-angled triangle or right triangle. The hypotenuse of a right triangle can be determined by the Pythagoras Theorem. This theorem gives the fundamental relationship between the three sides of a right triangle. It states that the sum of squares of the height and the base of a right triangle will be equal to the square of the hypotenuse. Moreover, the three sides of a right triangle are also known as Pythagorean triples. The formula for the Pythagoras theorem is given by: Hypotenuse2 = (Base2 + Height2) The steps to find the hypotenuse of a right triangle are given below:
Want to find complex math solutions within seconds? Use our free online calculator to solve challenging questions. With Cuemath, find solutions in simple and easy steps. Book a Free Trial Class Solved Examples on Hypotenuse CalculatorExample 1: Find the hypotenuse of a right-angled triangle if its base is 3 units and height is 4 units. Verify it using the online hypotenuse calculator. Solution: Hypotenuse = √(Base2 + Height2) = √(32 + 42) = √25 = 5 units. Example 2: Find the hypotenuse of a right-angled triangle if its base is 2.5 units and height is 3.2 units. Verify it using the online hypotenuse calculator. Solution: Hypotenuse = √(Base2 + Height2) = √(2.52 + 3.22) = √16.49 = 4.061 units. Now, you can try the hypotenuse calculator to find the hypotenuse of the triangles with the following dimensions:
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☛ Math Calculators:Pythagoras Over 2000 years ago there was an amazing discovery about triangles: When a triangle has a right angle (90°) ... ... and squares are made on each of the three sides, ... geometry/images/pyth2.js ... then the biggest square has the exact same area as the other two squares put together! It is called "Pythagoras' Theorem" and can be written in one short equation: a2 + b2 = c2 Note:
DefinitionThe longest side of the triangle is called the "hypotenuse", so the formal definition is: In a right angled triangle: Sure ... ?Let's see if it really works using an example. Example: A "3, 4, 5" triangle has a right angle in it.
Why Is This Useful?If we know the lengths of two sides of a right angled triangle, we can find the length of the third side. (But remember it only works on right angled triangles!) How Do I Use it?Write it down as an equation:
Example: Solve this triangleStart with:a2 + b2 = c2 Put in what we know:52 + 122 = c2 Calculate squares:25 + 144 = c2 25+144=169:169 = c2 Swap sides:c2 = 169 Square root of both sides:c = √169 Calculate:c = 13 Read Builder's Mathematics to see practical uses for this. Also read about Squares and Square Roots to find out why √169 = 13 Example: Solve this triangle.Start with:a2 + b2 = c2 Put in what we know:92 + b2 = 152 Calculate squares:81 + b2 = 225 Take 81 from both sides: 81 − 81 + b2 = 225 − 81 Calculate: b2 = 144 Square root of both sides:b = √144 Calculate:b = 12 Example: What is the diagonal distance across a square of size 1?Start with:a2 + b2 = c2 Put in what we know:12 + 12 = c2 Calculate squares:1 + 1 = c2 1+1=2: 2 = c2 Swap sides: c2 = 2 Square root of both sides:c = √2 Which is about:c = 1.4142... It works the other way around, too: when the three sides of a triangle make a2 + b2 = c2, then the triangle is right angled. Example: Does this triangle have a Right Angle?Does a2 + b2 = c2 ?
They are equal, so ... Yes, it does have a Right Angle! Example: Does an 8, 15, 16 triangle have a Right Angle?Does 82 + 152 = 162 ?
So, NO, it does not have a Right Angle Example: Does this triangle have a Right Angle?Does a2 + b2 = c2 ? Does (√3)2 + (√5)2 = (√8)2 ? Does 3 + 5 = 8 ? Yes, it does! So this is a right-angled triangle And You Can Prove The Theorem Yourself !Get paper pen and scissors, then using the following animation as a guide:
Another, Amazingly Simple, ProofHere is one of the oldest proofs that the square on the long side has the same area as the other squares. Watch the animation, and pay attention when the triangles start sliding around. You may want to watch the animation a few times to understand what is happening. The purple triangle is the important one. We also have a proof by adding up the areas. Historical Note: while we call it Pythagoras' Theorem, it was also known by Indian, Greek, Chinese and Babylonian mathematicians well before he lived. 511,512,617,618, 1145, 1146, 1147, 2359, 2360, 2361 How Do You Solve A and B in Pythagorean theorem?Pythagorean Theorem Formula. c=√a2+b2.. a=√c2−b2.. b=√c2−a2.. |