How to Find the Length of a Leg of a Right Triangle

The right triangle is a specific type of triangle. By definition, one of its angles is a right angle: 90 degrees. The side opposite the right angle is the hypotenuse, and it is the longest side. With these two bits of information we can apply the Pythagorean theorem to find the length of the leg of a right triangle.

Things You'll Need

• Paper
• Pencil

Instructions

1. Remember that there are three sides to a triangle, and that the hypotenuse is the longest side.

2. Revisit the Pythagorean theorem: the square of the hypotenuse is equal to the sum of the squares of the other two sides.

3. Name the sides of the triangle. Conventionally, the three letters used are a, b, and c, and the hypotenuse is always c. Using these letters, we can express the Pythagorean theorem as a^2+b^2=c^2, and if we know any two of the values of a, b and c, we can solve for the third variable.

4. Derive the formula for a side from the theorem. a= √c^2-b^2. If you are searching for b then the formula is b= √c^2-a^2.

5. Apply the given length of the hypotenuse and the known leg to the formula. For example, let c = 20 inches and a = 15 inches. Applying the formula we get:
   b=√20^2-15^2
   b=√400-225
   b=√175
   b=13.228

References

• clarku.edu: Right Triangles
• mathguide.com: Pythagorean Theorem