Pythagorean theorem: find the missing leg length

Learning Objectives Identify the legs and hypotenuse of a right triangle from a diagram. Recall and write the Pythagorean theorem formula: a² + b² = c². Substitute the known values of one leg and the hypotenuse into the theorem. Algebraically rearrange the Pythagorean theorem to isolate the variable for a missing leg. Calculate the length of a missing leg by using subtraction and finding the square root. Verify that their calculated leg length is shorter than the hypotenuse. Ever wondered how a carpenter makes sure a wall corner is perfectly square? 📐 They use the same secret math you're about to learn! This tutorial focuses on a key application of the Pythagorean theorem: finding the length of a missing leg in a right triangle when you already know one leg and the hy...

TermDefinitionExample Right TriangleA triangle that has one angle measuring exactly 90 degrees. This special angle is often marked with a small square.The corner of a square, a standard piece of paper, or a ramp meeting level ground. Legs (a and b)The two sides of a right triangle that form the 90-degree angle. They are always shorter than the hypotenuse.In a triangle with sides 3, 4, and 5, the legs are the sides with lengths 3 and 4. Hypotenuse (c)The longest side of a right triangle. It is always the side opposite the 90-degree angle.In a triangle with sides 3, 4, and 5, the hypotenuse is the side with length 5. Square of a NumberThe result of multiplying a number by itself. It is represented by a small 2 exponent (x²).The square of 8 is 8² = 8 × 8 = 64. Square RootA value that, when m...

Pythagorean Theorem a² + b² = c² This is the fundamental formula for all right triangles. It states that the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c). Formula to Find a Missing Leg a² = c² - b² or b² = c² - a² This is a rearranged version of the main theorem. To find a missing leg, you must subtract the square of the known leg from the square of the hypotenuse. Always start with the hypotenuse (c²).