Pythagorean Theorem What is it?? The Pythagorean Theorem describes the relationship between the side lengths in a right angle triangle.

What is a right triangle? hypotenuse leg right angle leg It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called legs. The side opposite the right angle is the hypotenuse.

The Pythagorean Theorem In a right triangle, if a and b are the measures of the legs and c is the hypotenuse, then a2 + b2 = c2. Note: The hypotenuse, c, is always the longest side.

1. Find the length of the hypotenuse if a = 12 and b = 16. c a a2 + b2 = c2 (12)2 + (16)2 = c2 144 + 256 = c2 400 = c2 Take the square root of both sides. 20 = c b

2. Find the length of the hypotenuse if a = 5 and b = 7. a2 + b2 = c2 (5)2 + (7)2 = c2 25 + 49 = c2 74 = c2 Take the square root of both sides. 8.6 = c c a b

Find the length of the leg, to the nearest tenth, if a = 4 and c = 10. a2 + b2 = c2 (4)2 + b2 = (10)2 16 + b2 = 100 Solve for b. 16 - 16 + b2 = 100 - 16 b2 = 84 b = 9.2 b

4. Find the length of the leg, to the nearest hundredth, if c = 10 and b = 7. a2 + b2 = c2 a2 + (7)2 = (10)2 a2 + 49 = 100 Solve for a. a2 = 100 - 49 a2 = 51 a = 7.1 c a b

a2 + b2 = c2 a2 + (3)2 = (15)2 a2 + 9 = 225 Solve for a. a2 = 225 - 9 Sample Problem: A 15 m ladder is propped against the side of a house. The base of the ladder is 3 m away from the house. How high up the wall does the ladder reach? a2 + b2 = c2 a2 + (3)2 = (15)2 a2 + 9 = 225 Solve for a. a2 = 225 - 9 a2 = 216 a = 14.7 m c= 15 m a=? b= 3m