Math calculator

Right Triangle Altitude Calculator

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.

Right Triangle Altitude inputs

Start with the given values

Understanding the reported Right Triangle Altitude

For a Right Triangle Altitude audit, retain Leg a and Leg b. Decide the likely direction of Altitude and segments before rerunning Right Triangle Altitude. Change only Leg b; the response in Altitude and segments can then be traced within the Right Triangle Altitude setup.

A sample Right Triangle Altitude run

Legs 6 and 8 give hypotenuse 10, altitude 4.8, and segments 3.6 and 6.4.

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.

Before accepting the Right Triangle Altitude result

Both legs must be positive. The altitude here is drawn from the right angle to the hypotenuse, not to a leg.

Reproducing Right Triangle Altitude later

Find c, equate areas ab/2=ch/2 for h, and use similar triangles for the projections.

When to reach for Right Triangle Altitude

What should remain consistent in Right Triangle Altitude

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.

These relationships appear in similar-triangle proofs, roof geometry, and distance constructions. A related application of Right Triangle Altitude is hypotenuse.

An independent Right Triangle Altitude check

Sketch Leg a before running Right Triangle Altitude. Place Leg b on the Right Triangle Altitude sketch and confirm its unit.

Test a symmetric Right Triangle Altitude case. In that Right Triangle Altitude case, compare Leg b with the expected Right Triangle Altitude scale.

Cross-checking Right Triangle Altitude

Substitute the calculated Altitude and segments into the defining Right Triangle Altitude relationship when that reversal is possible. The recovered value should agree with Leg a under Leg b. A mismatch points to rounding, entry order, or an assumption involving Leg b.

Questions about Right Triangle Altitude

Why is h=ab/c?

The two area formulas must agree.

Do the segments add to c?

Yes.

Can h exceed either leg?

No for a nondegenerate right triangle.