Objectives: The learner will..,

12.3 The Pythagorean Theorem Objectives: The learner will.., • Find a side length of a right triangle given the lengths of its other two sides. • Apply the Pythagorean Theorem to real-world problems. NCSCOS 1.02, 2.01

c a b 12.3 The Pythagorean Theorem Rules and Properties The Pythagorean Theorem a2 + b2 = c2 a and b are legs of a right triangle. c is the hypotenuse.

12.3 The Pythagorean Theorem Use the Pythagorean Theorem to find the length of a missing side of a right triangle in radical form 17 x x 10 15 24 152 + x2 = 172 242 + 102 =x2 225 + x2 = 289 x =26 x = 8

12.3 The Pythagorean Theorem Use the Pythagorean Theorem to find the length of a missing side of a right triangle in radical form. 4 6 3 2 x x 22 + x2 = 42 x2 + 32 = 62 4 + x2 = 16 x2 + 9 = 36

12.3 The Pythagorean Theorem Use the Pythagorean Theorem to find the length of a missing side of a right triangle in radical form. 15 x 4 5 x 8 52 + x2 = 152 82 + 42 = x2 25 + x2 = 225 64 + 16 = x2

12.3 The Pythagorean Theorem Use the Pythagorean Theorem to find the length of a missing side of a right triangle in radical form. 16 x 9 8 x 15 82 + x2 = 162 225 + 81 = x2 64 + x2 = 256

16200 8100  2 12.3 The Pythagorean Theorem A baseball diamond is a square with sides of 90 feet. In radical form, how long is it from third base to first base? x2 = 8100 + 8100 about 127.3 ft x2 = 16200 x x = x = 90 ft 90 ft

5000 2500  2 12.3 The Pythagorean Theorem A farmer has a chicken pen that is 50 yds by 50 yds square. In radical form, how far is it from one end of the pen to the other? 50 yds x2 = 502 + 502 x2 = 5000 x 50 yds x = x = about 70.7 yds across

x = 649800 x = 324900  2 12.3 The Pythagorean Theorem Two AF planes leave the same base, one travels north at 570 mph and the other plane travels east at 570 mph. After one hour, how far are the planes apart? x2 = 5702 + 5702 x 570 miles 570

x = 625 12.3 The Pythagorean Theorem Two boats leave the same dock, one boat travels north at 20 mph and the other boat travels west at 15 mph. After one hour, how long far would one boat travel to meet the other boat? x2 = 202 + 152 20 x =25 miles 15

12.3 The Pythagorean Theorem Complete the tables leaving in radical form 10 13 100 65 29 20

12.3 The Pythagorean Theorem Complete the table, leave in radical form (no decimals) 512 – 242 = 45 8 172 – 152 = 10 15 12

12.3 The Pythagorean Theorem n2 a2 + ( )2 = n2 Equilateral triangle: a2 + 22 = 42 n n a a2 = 42 – 22 a2 = 16 – 4 a2 = 12 n 2 n2 a = 2√3 n2 2 6 3 4 5 10 17

12.3 The Pythagorean Theorem Creating Pythagorean triples: A set of three positive integers that satisfy the Pythagorean Theorem, ex: {3, 4, 5}. If p and q are integers; p > q > 0, then follow the three-step process: For p = 2 & q = 1 {p2 – q2, 2pq, p2 + q2} {22 – 12, 2(2)(1), 22 + 12} {4 – 1, 4, 4 + 1} {3, 4, 5}

12.3 The Pythagorean Theorem {p2 – q2, 2pq, p2 + q2} Find the Pythagorean triples for: p = 4 & q = 3 p = 5 & q = 4 p = 6 & q = 5 p = 7 & q = 5 {7, 24, 25} There are an infinite # of Pythagorean triples! {9, 40, 41} {11, 60, 61} {24, 70, 74}

Objectives: The learner will..,