Home Building And Repairs

Figuring Longest Length of Right Triangles - Pythagorean Theorem


1.  Know the Sides:

Hypotenuse: This is the longest side, always opposite the right angle.

Legs: These are the two shorter sides that form the right angle.

2.  The Formula:

a² + b² = c²

a and b are the lengths of the legs.

c is the length of the hypotenuse (what we want to find).

3.  The Calculation:

Square the legs: Multiply the length of each leg by itself (e.g., if a leg is 3 feet long, 3² = 3 * 3 = 9).

Add the squares: Add the results from the previous step.

Find the square root: Use a calculator to find the square root of the sum. This is the length of the hypotenuse.

Example

Imagine you're building a roof and need to find the rafter length (the hypotenuse).

One leg (the rise) is 6 feet.

The other leg (the run) is 8 feet.

Calculation:

6² = 6 * 6 = 36
8² = 8 * 8 = 64
36 + 64 = 100
√100 = 10
The rafter length (hypotenuse) is 10 feet.

Tips for Construction

Use a Construction Calculator: Many calculators have a square root function (√) to make this easier.

Remember Common Triples: Familiarize yourself with Pythagorean triples like 3-4-5 or 6-8-10. This can help you quickly identify right angles.

Double-Check: Always double-check your measurements and calculations to avoid costly mistakes.

By following these simple steps, you can easily calculate the longest side of a right triangle and apply it to various construction measurements.

Back To Construction Math
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