Hypotenuse by Leg and Angle Calculator
Calculate hypotenuse length using trigonometry. Supports Degrees and Radians for Adjacent or Opposite legs.
DegreesRadians
About
When only one side and an acute angle are known, the Pythagorean theorem is insufficient. Trigonometry bridges this gap. This tool calculates the hypotenuse based on the position of the known leg relative to the known angle. It applies the Sine ratio for opposite legs and the Cosine ratio for adjacent legs. This is essential for navigation, vector physics, and machining where angular precision is required.
trigonometry
sine
cosine
geometry
triangle
Formulas
Depending on the selection, the tool uses one of the following logic paths:
{
Legsin(θ) if OppositeLegcos(θ) if Adjacent
Reference Data
| Known Leg Position | Trig Function | Formula |
|---|---|---|
| Opposite to Angle | Sine (sin) | c = a ÷ sin(θ) |
| Adjacent to Angle | Cosine (cos) | c = b ÷ cos(θ) |
Frequently Asked Questions
The Adjacent leg touches the angle you know (but is not the hypotenuse). The Opposite leg is across from the angle and does not touch it.
Yes. Use the toggle switch to change the input mode from Degrees (default) to Radians.