SOL 8.10 Pythagorean Theorem

For Right Triangles Only! What is a right triangle? A triangle with a 90 degree angle. Hypotenuse – always opposite the right angle; always the longest side leg leg

Pythagorean Theorem The Pythagorean Theorem states: a2 + b2 = c2 Hypotenuse (c) Leg (a) Leg (b)

Example 1 Solve for x. a2 + b2 = c2 62 + 82 = x2 36 + 64 = x2 100 = x2

Example 2 Solve for y. a2 + b2 = c2 72 + 42 = y2 49 + 16 = y2 65 = y2

Your Turn! Use the Pythagorean Theorem to solve. Round to the nearest tenth, if necessary. Legs: 12 and 9 15 Legs: 16 and 12 20 Legs: 100 and 200 223.6

To the nearest tenth of a foot, find the length of the diagonal of a rectangle with a width of 4 feet and a length of 10 feet. a2 + b2 = c2 42 + 102 = x2 16 + 100 = x2 116 = x2 √116 = √x2 x = 10.8 x 4 ft 10 ft

Tonight’s Homework! Legs: 4 and 5 Legs: 9 and 5 Legs: 7 and 12 Solve. Round to the nearest tenth, if necessary! Answers Legs: 4 and 5 Legs: 9 and 5 Legs: 7 and 12 Legs: 24 and 32 Legs: 15 and 8 Legs: 0.4 and 0.3 Legs: 20 and 21 Legs: 7.2 and 9.6 6.4 10.3 13.9 40 17 0.5 29 12