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Geometry Academic

Geometry Academic. UNIT QUESTION: What patterns can I find in right triangles? Standard: MM2G1, MM2G2 Today ’ s Question: How do we solve 45°-45°-90° right triangles? Standard: MM2G1.b. Special Right Triangles. You will be able to find the lengths of sides of special right triangles.

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Geometry Academic

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  1. Geometry Academic UNIT QUESTION: What patterns can I find in right triangles? Standard: MM2G1, MM2G2 Today’s Question: How do we solve 45°-45°-90° right triangles? Standard: MM2G1.b

  2. Special Right Triangles You will be able to find the lengths of sides of special right triangles 45-45-90 And 30-60-90

  3. 45-45-90

  4. We will use a reference triangle to set up a proportion then solve. In a 45-45-90 triangle… LEGS ARE THE SAME LENGTH

  5. 45-45-90 Right Triangle 1 1 This is our reference triangle for the 45-45-90.

  6. 45-45-90 Right Triangle x x

  7. Special Right Triangles Leg:Leg:Hypotenuse

  8. EX: 1 Solve for x a√2 x a 3 a 3

  9. EX: 2 Solve for x x a√2 a 5 a 5

  10. EX: 3 Solve for x 45 3 a√2 a x a

  11. Extension Problem The diagonal of a square is 12 inches. Find the area. Round to the nearest tenth. 12 in. Area = 72 in.2

  12. Extension Problem 2 Given a circle with a diameter of 12 inches, find the length of the hypotenuse of a right triangle with the right angle at the center. X 12 inches

  13. Real Life Problem

  14. 30-60-90

  15. We will use a reference triangle to set up a proportion then solve. 30-60-90 Right Triangle 60 2 1 30 This is our reference triangle for the 30-60-90 triangle.

  16. Special Right Triangles Short Leg:Long Leg:Hypotenuse

  17. Ex: 1 Solve for x and y. 60 8 2a x a 30 y a√3

  18. Solve for x and y Ex: 2 y a√3 30 x a 2a 24 60

  19. Ex: 3 Solve for x and y. 30 2a 14 y a√3 60 x a y = 7√3 x = 7

  20. Ex: 4 Solve for x and y a x a√3 60 30 y 2a y = 10 x = 5

  21. Extension Problem The altitude of an equilateral triangle is 8 inches. Find the perimeter of the triangle. 30° 2a a√3 8 60° a a = 4.168 in., so 2a = 9.238 in. Perimeter = 27.71 inches

  22. Real Life Problem D A 30° 30° C B 90 feet. • A person is standing at point A cheering on his favorite team. Round to nearest tenth. • Find the height CD of the bleachers. • Find the height of the fan at Point A from the ground. • Find the distance AB that the fan is from the field at B. 52.0 feet 39.0 feet 77.9 feet

  23. Homework Page 557, and 562

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