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SOL 8.10 cont.

SOL 8.10 cont. Pythagorean Theorem. Review. Previously, we used the Pythagorean Theorem to find the hypotenuse of a right triangle. (a 2 + b 2 = c 2 ) We were given a and b and found c !

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SOL 8.10 cont.

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  1. SOL 8.10 cont. Pythagorean Theorem

  2. Review • Previously, we used the Pythagorean Theorem to find the hypotenuse of a right triangle. (a2 + b2 = c2) • We were given a and b and found c! • What happens if we are given one of the legs and the hypotenuse, and are asked to find the measurement for the second leg? • If we are given a and c, or b and c, we can find the missing leg!

  3. Example 3 • Solve for a. • a2 + b2 = c2 • a2 + 62 = 152 • a2 + 36 = 225 - 36 -36 • a2 = 189 • √a2 = √189 • a = 13.7 6 a 15

  4. Example 4 • Solve for b. • a2 + b2 = c2 • 72 + b2 = 162 • 49 + b2 = 256 -49 -49 • b2 = 207 • √b2 = √207 • b = 14.4 16 7 b

  5. Your Turn! Use the Pythagorean Theorem to solve. Round to the nearest tenth, if necessary. • b = 9, c = 12 7.9 • a = 3, c = 8 7.4 • a = 15, b = 18 23.4

  6. Pythagorean Triple • A Pythagorean Triple is three positive integers, a, b, and c, where a2 + b2 = c2. • Example: 3, 4, 5 32 + 42 = 52 9 + 16 = 25 25 = 25 • Example: 5, 12, 13 52 + 122 = 132 25 + 144 = 169 169 = 169 • 3 4 5 5 12 13 7 24 25 6 8 10 10 24 26 14 48 50 9 12 15 15 36 39 21 72 75 12 16 20 20 48 52 28 96 100

  7. Identifying a Right Triangle! • A triangle is a right triangle if the sides of a triangle have lengths a, b, and c such that a2 + b2 = c2. (Hint: remember c is always the longest side.) • Ex: The measures of three sides of a triangle are 15 inches, 8 inches, and 17 inches. Determine whether the triangle is a right triangle. 152 + 82 = 172 225 + 64 = 289 289 = 289 since they are equal the triangle must be a right triangle

  8. Your Turn! Determine if the following sides make a right triangle by using the Pythagorean Theorem? • 18, 24, and 30 Yes (900 = 900) • 4, 7, and 5 No (41 ≠ 49)

  9. Tonight’s Homework! Solve. Round to the nearest tenth, if necessary! Determine if the following are right triangles? Show your work! b = 15, c = 25 a = 10, c = 25 b = 14, c = 20 b = 17, c = 20 a = 3, c = 8 b = 3.4, c = 8.6 a = 15, b = 18 9, 40, 41 45, 26, 53 1.6, 6.5, 6.3

  10. Answers to HW • 20 • 22.9 • 14.3 • 10.5 • 7.4 • 7.9 • 23.4 • Yes (1681 = 1681) • No (2701 = 2809) • Yes (42.25 = 42.25)

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