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

4. In a 45-45-90 triangle… We will use a reference triangle to set up a proportion then solve.

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. Leg:Leg:Hypotenuse

8. 3 3 x EX: 1 Solve for x a√2 a a

9. 5 5 x EX: 2 Solve for x a√2 a a

10. x 3 45 EX: 3 Solve for x a√2 a a

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

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. 12 inches X

13. Real Life Problem

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

16. Short Leg:Long Leg:Hypotenuse

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

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

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

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

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

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

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