Leg Rule Calculator

Last updated: 26 Mar 2025 | Author: Brij | Review By: Irshad

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This tool calculates the length of a leg in a right triangle using the Leg Rule (geometric mean theorem). Input the hypotenuse and projection lengths, select units, and get the leg length instantly.

Hypotenuse (c):

Projection of Leg A (p₁):

Projection of Leg B (p₂):

Result

Leg A (a):

Leg B (b):

What is the Leg Rule?

The Leg Rule is a fundamental concept in geometry used to calculate the legs of a right triangle when given the hypotenuse and projections. This rule is useful in construction, engineering, and various mathematical applications.

The formula for finding the legs of a right triangle is:

$\text{Leg A} = \sqrt{\text{Hypotenuse} \times \text{Projection of A}}$

$\text{Leg B} = \sqrt{\text{Hypotenuse} \times \text{Projection of B}}$

Why Use a Leg Rule Calculator?

This calculator simplifies the process by allowing users to input values for the hypotenuse and projections to get the leg lengths instantly. It eliminates manual calculations and reduces errors.

Step-by-Step Calculation

Input the Values:

Hypotenuse ( $H$ )
Projection of A ( $P_A$ )
Projection of B ( $P_B$ )

Apply the Leg Rule Formula:

$\text{Leg A} = \sqrt{H \times P_A}$
$\text{Leg B} = \sqrt{H \times P_B}$

Convert the Results (if needed):

The calculator supports multiple units and converts results accordingly.

Example Calculation

Given:

Hypotenuse = 10 inches
Projection A = 6 inches
Projection B = 4 inches

Using the Formula:

$\text{Leg A} = \sqrt{10 \times 6} = \sqrt{60} \approx 7.75 \text{ inches}$

$\text{Leg B} = \sqrt{10 \times 4} = \sqrt{40} \approx 6.32 \text{ inches}$

Conclusion

The Leg Rule Calculator is a fast and reliable tool for calculating triangle legs using the hypotenuse and projections. It’s especially useful for students, engineers, and construction professionals working with right triangles. Try it out to make your calculations quick and accurate!

FAQ

Where is the "Leg Rule" used?

It is mainly used in geometry, engineering, and construction work, where calculating the legs of a right triangle accurately is essential.

How does the "Leg Rule" work?

This rule is related to the Pythagorean theorem. By using the values of the hypotenuse and projections, you can easily calculate both legs of a triangle.

Why is the "Leg Rule" important?

This rule simplifies complex triangle calculations and saves time, especially for those who regularly work with such measurements.

Check out 1 similar Leg Rule Calculator :

Leg Rule Calculator

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