- Hypotenuse
- 5
How it works
Scaling preserves the right-angle relationship
A 3–4–5 triangle and a 6–8–10 triangle satisfy the same relationship because every side doubles. Their areas differ by a factor of four, so doubling a diagonal does not merely double the enclosed area.
Identifying the hypotenuse correctly
The Pythagorean theorem applies to a right triangle. The hypotenuse is opposite the right angle and is the longest side, so it cannot be interchanged with a leg when choosing the unknown. Use consistent length units for all sides. A valid arithmetic result does not establish that a measured triangle actually has a right angle.
Find hypotenuse: formula and assumptions
c = √(a²+b²).
The two entered sides must be perpendicular legs.
Find a leg: formula and assumptions
b = √(c²−a²).
The hypotenuse must be longer than the known leg.
Worked example
Using the Find hypotenuse example:
- Leg a
- 3
- Leg b
- 4
c = √(a²+b²).
Example result
Hypotenuse: 5
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
Can I use this formula for any triangle?
No. The equation a² + b² = c² applies when the legs meet at a right angle.
Why must the hypotenuse be longer than the known leg?
The missing leg uses the square root of c² − a². A nonpositive difference cannot form a nondegenerate right triangle.
Prepared by Finflo. See our methodology and editorial policy.