What Is FREE TOOLS Hypotenuse Calculator?
A Hypotenuse Calculator is a free online tool used to calculate the hypotenuse of a right triangle when the lengths of the other two sides are known.
The hypotenuse is always the longest side of a right triangle and is located directly opposite the 90° angle.
Hypotenuse Formula
a2+b2=c2a^2 + b^2 = c^2
c=15.02+15.02=21.21c=\sqrt{\text{15.0}^2+\text{15.0}^2}=\text{21.21}c=15.02+15.02=21.21
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The calculator uses the Pythagorean Theorem:a2+b2=c2\boxed{a^2+b^2=c^2}
To find the hypotenuse cc, rearrange the formula:c=a2+b2\boxed{c=\sqrt{a^2+b^2}}
Where:
- a = first leg
- b = second leg
- c = hypotenuse
Example
Suppose a right triangle has:
- Side a=6a=6
- Side b=8b=8
The hypotenuse is:c=62+82c=\sqrt{6^2+8^2}c=36+64c=\sqrt{36+64}c=100c=\sqrt{100}c=10c=10
Therefore, the hypotenuse is 10 units.
How Does a Hypotenuse Calculator Work?
A FREE TOOLS Hypotenuse Calculator typically requires you to enter the lengths of the two legs of a right triangle.
The calculator then:
- Squares the first side.
- Squares the second side.
- Adds the two squared values.
- Calculates the square root.
- Returns the hypotenuse.
When Should You Use a Hypotenuse Calculator?
It can be useful for:
- Geometry homework
- Trigonometry problems
- Construction measurements
- Architecture
- Engineering
- Surveying
- Calculating diagonal distances
- Measuring ramps and slopes
- Checking right-triangle calculations
Hypotenuse vs. Other Triangle Sides
In a right triangle:
- Hypotenuse = longest side
- Leg = either of the two sides forming the 90° angle
- Right angle = exactly 90°
The hypotenuse is always opposite the right angle.
Important Note
The Pythagorean Theorem applies only to right triangles. If the triangle does not contain a 90° angle, a standard hypotenuse calculation using a2+b2=c2a^2+b^2=c^2 is not appropriate.
Also, the two input sides should use the same unit, such as inches, feet, meters, or centimeters.
In Simple Terms
A FREE TOOLS Hypotenuse Calculator quickly finds the longest side of a right triangle using:c=a2+b2\boxed{c=\sqrt{a^2+b^2}}
Simply enter the lengths of the two legs, and the calculator calculates the hypotenuse automatically.
It is a convenient free tool for students, teachers, builders, engineers, architects, and anyone working with right triangles.
