# Right Triangle Calculator

> Solve a right triangle from two known values and calculate all sides, acute angles, altitude, area, and perimeter.

Page: https://askcalculators.com/calculator/right-triangle-calculator/
Definition: https://askcalculators.com/calculator/right-triangle-calculator/definition.json
JSON Schema: https://askcalculators.com/calculator/right-triangle-calculator/schema.json
Version: 2.0.0
Maintained by: AskCalculators (software project; not a credentialed reviewer)
Qualified review: pending. Automated checks do not establish professional approval.
Page status: Live
Review status: Pending

## Use
Open the calculator page and enter values. Query-string parameters can restore and bookmark a calculation.
Example: https://askcalculators.com/calculator/right-triangle-calculator/?mode=legs&legA=3&legB=4&angleUnit=degrees

## Inputs
- mode: Known values; type=select; required; default=legs; values=legs|leg-hypotenuse|hypotenuse-angle|leg-angle|area-leg
- legA: Leg a; type=number; required; default=3; min=0.000001; showWhen=mode:legs
- legB: Leg b; type=number; required; default=4; min=0.000001; showWhen=mode:legs
- knownLeg: Known leg a; type=number; required; default=3; min=0.000001; showWhen=mode:leg-hypotenuse
- knownHypotenuse: Hypotenuse c; type=number; required; default=5; min=0.000001; showWhen=mode:leg-hypotenuse
- angleHypotenuse: Hypotenuse c; type=number; required; default=5; min=0.000001; showWhen=mode:hypotenuse-angle
- angleAlpha: Angle α; type=number; required; default=36.869897; min=0.000001; showWhen=mode:hypotenuse-angle
- angleLeg: Leg a; type=number; required; default=3; min=0.000001; showWhen=mode:leg-angle
- legAngleAlpha: Angle α; type=number; required; default=36.869897; min=0.000001; showWhen=mode:leg-angle
- areaInput: Area; type=number; required; default=6; min=0.000001; showWhen=mode:area-leg
- areaLeg: Leg a; type=number; required; default=3; min=0.000001; showWhen=mode:area-leg
- angleUnit: Angle input unit; type=select; required; default=degrees; values=degrees|radians

## Outputs
- sideA: Leg a; format=number; primary
- sideB: Leg b; format=number
- hypotenuse: Hypotenuse c; format=number
- angleAlphaResult: Angle α; format=number
- angleBetaResult: Angle β; format=number
- altitude: Altitude to hypotenuse; format=number
- area: Area; format=number
- perimeter: Perimeter; format=number

## Formula
a²+b²=c²; α=atan(a/b); β=90°−α; area=ab/2; altitude h=ab/c.

## Rules
- Empty optional inputs are undefined, not zero.
- Hidden conditional inputs are ignored.
- Do not invent missing required inputs.