Find the altitude to the hypotenuse and its two projection segments from the legs. Each submitted value produces altitude and segments plus the intermediate reasoning.
These relationships appear in similar-triangle proofs, roof geometry, and distance constructions. A related application of Right Triangle Altitude is hypotenuse.
For a right triangle, c=√(a²+b²), altitude h=ab/c, and the hypotenuse segments are a²/c and b²/c. Right Triangle Altitude also connects with right-triangle inradius.
This definition sets the boundary between right triangle altitude and a neighboring calculation with similar inputs.
Legs 6 and 8 give hypotenuse 10, altitude 4.8, and segments 3.6 and 6.4.
Both legs must be positive. The altitude here is drawn from the right angle to the hypotenuse, not to a leg.
An impossible altitude and segments sign or magnitude usually points to field assignment before it points to rounding.
Find c, equate areas ab/2=ch/2 for h, and use similar triangles for the projections.
Start the right triangle altitude setup by pairing every source number with leg a and leg b. Convert unlike units before typing, and postpone rounding until the displayed altitude and segments is ready to report.
Scaling both legs equally scales every linear result by the same factor. Use that direction of change to check the displayed altitude and segments before copying it elsewhere.
The Pythagorean calculator finds c; this page continues to the altitude and projections. Keep that boundary in mind when interpreting the numerical result.
When copying the result elsewhere, include its label and any squared, linear, angular, or percentage unit implied by the inputs. That record distinguishes a calculated altitude and segments from an unlabeled number and makes later checking substantially easier.
For later verification, record leg a and leg b before rounding the altitude and segments. The unrounded working value can feed subsequent steps while the rounded value serves presentation.
The two projection segments must add to the hypotenuse, and their product must equal the altitude squared. Verify both identities after rounding.
For Right Triangle Altitude, after checking the sample, vary one meaningful input and predict the direction of change before recalculating. A result that moves oppositely deserves review. Label the final value with its geometric or algebraic role so it is not confused with a neighboring length, area, root, or coefficient.
The two area formulas must agree.
Yes.
No for a nondegenerate right triangle.