Pythagorean Theorem Application

Using the Pythagorean Theorem for Measurement Two airplanes leave the same airport at the same time. The first plane flies to a landing strip 350 miles south, while the other plane flies to an airport 725 miles west. How far apart are the two planes after they land? a2 + b2 = c2 Pythagorean Theorem 3502 + 7252 = c2 Substitute for a and b. 122,500 + 525,625 = c2 Simplify powers. 648,125 = c2 Add. Find the positive square root. 805 ≈ c The two planes are approximately 805 miles apart.

Try This! Two birds leave the same spot at the same time. The first bird flies to his nest 11 miles south, while the other bird flies to his nest 7 miles west. How far apart are the two birds after they reach their nests? a2 + b2 = c2 Pythagorean Theorem 112 + 72 = c2 Substitute for a and b. 121 + 49 = c2 Simplify powers. 170 = c2 Add. Find the positive square root. 13 ≈ c The two birds are approximately 13 miles apart.

Converse of the Pythagorean Theorem The converse of the Pythagorean Theorem states that any three nonzero whole numbers that make the equation true are the sides lengths of a right triangle. These numbers are called Pythagorean triples. a2 + b2 = c2 Determine whether the set of numbers will form a right triangle. A. 9, 40, 41 a2 + b2 = c2 Use Pythagorean Theorem 92 + 402 = 412 Substitute for a , b and c. Remember c must be the largest number. 81 + 1600 = 1681 Determine if it is a true statement 1681 = 1681 Yes, this set of numbers forms a right triangle. B. 5, 7, 3 a2 + b2 = c2 Use Pythagorean Theorem Substitute for a , b and c. Remember c must be the largest number. 32 + 52 = 72 9 + 25 = 49 Determine if it is a true statement 34 ≠ 49 No, this set of numbers does not forms a right triangle.

Converse of the Pythagorean Theorem Try This! Determine whether the set of numbers will form a right triangle. A. 5, 12, 13 Use Pythagorean Theorem a2 + b2 = c2 52 + 122 = 132 Substitute for a , b & c. Remember c must be the largest number. 25 + 144 = 169 Determine if it is a true statement 169 = 169 Yes, this set of numbers forms a right triangle. A. 3, 6, 9 a2 + b2 = c2 Use Pythagorean Theorem Substitute for a , b and c. Remember c must be the largest number. 32 + 62 = 92 9 + 36 = 81 Determine if it is a true statement 45 ≠ 81 No, this set of numbers does not forms a right triangle.

Lesson Quiz Use the figure for Problems 1 and 2. 1. Find the height h of the triangle. 8 m 2. Find the length of side c to the nearest meter. 10 m c h 12 m 3. An escalator in a shopping mall is 40 ft long and 32 ft tall. What distance does the escalator carry shoppers? 6 m 9 m 2624 ≈ 51 ft