Pythagorean theorem: find the missing leg length

Learning Objectives Identify the legs and hypotenuse in any right-angled triangle. Recall and state the Pythagorean theorem formula. Rearrange the Pythagorean theorem to solve for the square of a missing leg. Apply inverse operations (squaring and square rooting) to find actual leg lengths. Calculate the length of a missing leg in a right triangle given the other leg and the hypotenuse. Solve real-world problems involving finding a missing leg length. Imagine you're building a ramp 🏗️! You know how long the ramp is and how high it reaches, but how far out does it stretch along the ground? That's what we'll figure out today! In this lesson, you'll learn how to use the powerful Pythagorean theorem to find the length of a missing side in a right-angled tria...

TermDefinitionExample Right TriangleA triangle that has one angle exactly equal to 90 degrees.A triangle with angles 30°, 60°, and 90° is a right triangle. LegsThe two shorter sides of a right triangle that form the 90-degree (right) angle.In a right triangle with sides 3, 4, and 5, the sides of length 3 and 4 are the legs. HypotenuseThe longest side of a right triangle, always located directly opposite the 90-degree angle.In a right triangle with sides 3, 4, and 5, the side of length 5 is the hypotenuse. SquareThe result of multiplying a number by itself. Represented by a small '2' as an exponent (e.g., $x^2$).The square of 7 is $7^2 = 7 imes 7 = 49$. Square RootThe inverse operation of squaring a number; finding the number that, when multiplied by itself, gives the original n...

Pythagorean Theorem $a^2 + b^2 = c^2$ This formula relates the lengths of the two legs ($a$ and $b$) to the length of the hypotenuse ($c$) in any right-angled triangle. It's the foundation for finding any missing side. Finding a Missing Leg (Rearranged Theorem) $a^2 = c^2 - b^2$ (or $b^2 = c^2 - a^2$) When you know the hypotenuse ($c$) and one leg ($b$), and you need to find the other leg ($a$), you can rearrange the Pythagorean theorem. You subtract the square of the known leg from the square of the hypotenuse to find the square of the missing leg.