Hypotenuse of a Right Triangle in Feet Calculator
Calculate the length of a right triangle’s hypotenuse using the Pythagorean theorem
Hypotenuse Calculator
Result:
Hypotenuse (c) = 0 feet
The Pythagorean Theorem
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of squares of the other two sides (a and b).
c² = a² + b²
c = √(a² + b²)
Where:
- c is the length of the hypotenuse (in feet)
- a is the length of the base (in feet)
- b is the height (in feet)
* A right triangle has one angle that is exactly 90 degrees (a right angle).
Interactive Visualization
This visualization updates as you change the base and height values. The hypotenuse is shown in red.
* Move the sliders to adjust the triangle dimensions and see how the hypotenuse changes.
Practical Applications
Construction
Used for determining diagonal bracing lengths, roof pitches, and ensuring right angles in framing.
Carpentry
Essential for measuring diagonal cuts, calculating stair dimensions, and ensuring square corners.
Land Surveying
Used to measure distances across inaccessible areas and calculate property boundaries.
Engineering
Applied in structural analysis, determining forces in trusses, and designing support systems.
The 3-4-5 Rule
Construction professionals often use the 3-4-5 rule to quickly establish a right angle:
- Mark a point 3 feet along one wall
- Mark a point 4 feet along the perpendicular wall
- If the diagonal between these points is exactly 5 feet, you have a perfect right angle
This is a practical application of the Pythagorean theorem: 3² + 4² = 5²
Frequently Asked Questions
What is the hypotenuse of a right triangle?
The hypotenuse is the longest side of a right triangle, which is always opposite to the right angle (90-degree angle).
Why is the Pythagorean theorem important?
The theorem provides a fundamental relationship in Euclidean geometry and has countless applications in construction, engineering, physics, and everyday problem-solving.
How accurate is this calculator?
This calculator provides results accurate to several decimal places, which is sufficient for most practical applications. For extremely precise work, consider rounding as appropriate for your specific needs.
Can I use this for non-right triangles?
No, the Pythagorean theorem only applies to right triangles. For non-right triangles, you would need to use other formulas such as the Law of Cosines.
Example Calculations
Example 1: Standard 3-4-5 Triangle
Given:
- Base (a) = 3 feet
- Height (b) = 4 feet
Solution:
c = √(a² + b²)
c = √(3² + 4²)
c = √(9 + 16)
c = √25
c = 5 feet
Example 2: Roof Pitch Calculation
Given:
- Half the span (a) = 12 feet
- Rise (b) = 8 feet
Solution:
Rafter length (c) = √(a² + b²)
c = √(12² + 8²)
c = √(144 + 64)
c = √208
c ≈ 14.42 feet
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