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MIA U1D12 Warm Up:

MIA U1D12 Warm Up: The distance from Raleigh to Wilmington is 120 miles, the distance from Wilmington to Charlotte is 200 miles, and the distance from Raleigh to Charlotte is 160 miles. Do the three towns form a right triangle? Explain.

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MIA U1D12 Warm Up:

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  1. MIA U1D12 Warm Up: The distance from Raleigh to Wilmington is 120 miles, the distance from Wilmington to Charlotte is 200 miles, and the distance from Raleigh to Charlotte is 160 miles. Do the three towns form a right triangle? Explain. Yes; The Pythagorean Theorem is true for these three values. 1602 + 1202 = 2002

  2. Homework Check:

  3. Homework Check:

  4. REMINDER from yesterday… YOU learnedto use the Pythagorean Theorem and its converse to solve problems.

  5. Vocabulary Pythagorean Theorem: See next slide a2 + b2 = c2 Leg: The sides of a right triangle that include the right angle. Hypotenuse: In a right triangle, the side opposite the right angle.

  6. a2 + b2 = c2

  7. 41 = c Solve for c; c = c2. Find the length of the hypotenuse. c A. 4 5 Pythagorean Theorem a2 + b2 = c2 42 + 52 = c2 Substitute for a and b. Simplify powers. 16 + 25 = c2 41 = c2 6.40c

  8. Solve for c; c = c2. 225 = c Find the length of the hypotenuse. triangle with coordinates B. (1, –2), (1, 7), and (13, –2) Pythagorean Theorem a2 + b2 = c2 Substitute for a and b. 92 + 122 = c2 Simplify powers. 81 + 144 = c2 15= c

  9. 74 = c Solve for c; c = c2. Find the length of the hypotenuse. c A. 5 7 Pythagorean Theorem a2 + b2 = c2 52 + 72 = c2 Substitute for a and b. Simplify powers. 25 + 49 = c2 8.60c

  10. y x Solve for c; c = c2. 61 = c Find the length of the hypotenuse. B. triangle with coordinates (–2, –2), (–2, 4), and (3, –2) (–2, 4) The points form a right triangle. a2 + b2 = c2 Pythagorean Theorem 62 + 52 = c2 Substitute for a and b. 36 + 25 = c2 Simplify powers. (3, –2) (–2, –2) 7.81c

  11. 576 = 24 units Solve for the unknown side in the right triangle. Pythagorean Theorem a2 + b2 = c2 25 Substitute for a and c. 72 + b2 = 252 b Simplify powers. 49 + b2 = 625 –49 –49 b2 = 576 7 b = 24

  12. 128 11.31 units Solve for the unknown side in the right triangle. a2 + b2 = c2 Pythagorean Theorem 12 Substitute for a and c. b 42 + b2 = 122 Simplify powers. 16 + b2 = 144 –16 –16 4 b2 = 128 b 11.31

  13. a = 20 units ≈ 4.47 units 1 2 1 2 A = hb= (8) ( 20) = 4 20 units2 17.89 units2 Use the Pythagorean Theorem to find the height of the triangle. Then use the height to find the area of the triangle. a2 + b2 = c2 Pythagorean Theorem Substitute for b and c. a2 + 42 = 62 a2 + 16 = 36 6 6 a a2 = 20 4 4 Find the square root of both sides.

  14. a = 21 units ≈ 4.58 units 1 2 1 2 A = hb = (4) ( 21) = 2 21 units2 9.17 units2 Use the Pythagorean Theorem to find the height of the triangle. Then use the height to find the area of the triangle. a2 + b2 = c2 Pythagorean Theorem a2 + 22 = 52 Substitute for b and c. 5 5 a2 + 4 = 25 a a2 = 21 2 2 Find the square root of both sides.

  15. QUIZ TIMED….You have 10 minutes…SHOW YOUR WORK

  16. TOPIC: Solving for a Variable Objective: To solve equations and formulas for a specified variable.

  17. Example 1: Solve for x. SYW: 3ax – b = d – 4cx x = (b + d) 3a + 4c

  18. Example 2: Solve for x. SYW: x + 3ab = ax + n x = n – 3ab 1 - a

  19. Example 3: Solve for w. SYW: P = 2l + 2w w = P – 2l 2

  20. Classwork 1: Practice – Solving Literal Equations #1-8

  21. Classwork 2: Applications of Volume Formulas #3

  22. Homework: • Practice – Solving Literal Equations #9-16

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