Leg of a Triangle — Definition, Formula & Examples
A leg of a triangle is one of the two shorter sides of a right triangle that form the right angle. The third side, opposite the right angle, is called the hypotenuse.
In a right triangle, each of the two sides adjacent to (and forming) the 90° angle is called a leg. The legs are distinct from the hypotenuse, which is the side opposite the right angle and always the longest side of the triangle.
Key Formula
Where:
- = Length of one leg
- = Length of the other leg
- = Length of the hypotenuse
How It Works
Every right triangle has exactly two legs and one hypotenuse. The legs meet at the vertex where the 90° angle is located. When you use the Pythagorean theorem, the two values you square and add together are the lengths of the legs. In many problems, one leg is called the base and the other the height, which makes calculating the triangle's area straightforward: .
Worked Example
Problem: A right triangle has one leg of length 6 and a hypotenuse of length 10. Find the length of the other leg.
Write the Pythagorean theorem: Substitute the known values into the formula.
Simplify: Square the known sides.
Solve for b: Subtract 36 from both sides, then take the square root.
Answer: The other leg has a length of 8.
Why It Matters
Identifying the legs of a right triangle is essential whenever you apply the Pythagorean theorem, use trigonometric ratios (sine, cosine, tangent), or calculate a triangle's area. These skills appear constantly in geometry courses and in practical fields like construction and engineering.
Common Mistakes
Mistake: Confusing a leg with the hypotenuse when plugging into the Pythagorean theorem.
Correction: The hypotenuse is always the longest side and sits opposite the right angle. The two shorter sides that form the right angle are the legs. Make sure the hypotenuse goes on its own side of the equation (), not added with a leg.