1. 10-2 The Pythagorean Theorem Hubarth Algebra

2. leg hypotenuse Pythagorean Theorem In any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a b c

3. What is the length of the hypotenuse of this triangle? a 2 + b 2 = c 2 8 2 + 15 2 = c 2 64 + 225 = c 2 17 = c The length of the hypotenuse is 17 m. 289 = c 2 Ex 1 Using the Pythagorean Theorem

4. A toy fire truck is positioned so that the base of the ladder is 13 cm from the wall. The ladder is extended 28 cm to the wall. How high above the table is the top of the ladder? Define:Let b = height (in cm) of the ladder from a point 9 cm above the table. Relate:The triangle formed is a right triangle. Use the Pythagorean Theorem. Ex 2 Application a 2 + b 2 = c 2 13 2 + b 2 = 28 2 169 + b 2 = 784 b 2 = 615 b 24.8 The height to the top of the ladder is 9 cm higher than 24.8 cm, so it is about 33.8 cm from the table.

5. Ex 3 Using the converse of the Pythagorean Theorem Determine whether the given lengths can be sides of a right triangle. a. 5 in., 5 in., and 7 in. This triangle is not a right triangle. b. 10 cm, 24 cm, and 26 cm This triangle is a right triangle. 100 + 576 676 676 = 676 10 2 + 24 2 26 2 5 2 + 5 2 7 2 25 + 25 49 50 = 49 /

6. Practice 1. What is the length of the hypotenuse of a right triangle with legs of lengths 7cm and 24cm? 25cm 2. Solve for b in the right triangle. 4mi 8mi b 3. A triangle has sides of lengths 10m, 24m and 26m. Is the triangle a right triangle? Yes