Pythagorean theorem: find the length of the hypotenuse

Learning Objectives Identify the hypotenuse in a right-angled triangle. State the Pythagorean theorem formula ($a^2 + b^2 = c^2$). Substitute the lengths of the legs into the Pythagorean theorem. Calculate the square of a number and find the square root of a number. Apply the Pythagorean theorem to find the length of the hypotenuse. Solve real-world problems involving finding the hypotenuse of a right triangle. Ever wondered how construction workers know the exact length of a diagonal brace for a wall, or how far it is to walk across a park diagonally? 🚶‍♀️📐 In this lesson, you'll discover the amazing Pythagorean theorem, a powerful tool for working with right-angled triangles. We'll focus specifically on how to use it to find the longest side, called the hypote...

TermDefinitionExample Right TriangleA triangle that has one angle exactly equal to 90 degrees (a right angle).A triangle with angles 30°, 60°, and 90° is a right triangle. Right AngleAn angle that measures exactly 90 degrees. It is often marked with a small square symbol in the corner.The corner of a square or a book forms a right angle. Legs (of a Right Triangle)The two shorter sides of a right triangle that form the right angle. They are often labeled 'a' and 'b'.If a right triangle has sides of length 3 cm, 4 cm, and 5 cm, then 3 cm and 4 cm are the legs. HypotenuseThe longest side of a right triangle, always opposite the right angle. It is often labeled 'c'.In a right triangle with sides 3 cm, 4 cm, and 5 cm, the 5 cm side is the hypotenuse. Squaring a Nu...

Pythagorean Theorem $a^2 + b^2 = c^2$ This fundamental theorem states that in any right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the two legs (a and b). It is used to find an unknown side length when two other side lengths are known. Formula for Finding the Hypotenuse $c = \sqrt{a^2 + b^2}$ This is a rearrangement of the Pythagorean theorem specifically for finding the length of the hypotenuse (c) when the lengths of the two legs (a and b) are known. You first square the legs, add them, and then take the square root of the sum.