Two special right triangles determined by... measures. Two special right triangles determined by... measures

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3 Two special right triangles determined by... measures Two special right triangles determined by... measures

4 Two special right triangles determined by... measures Two special right triangles determined by... measures

5 Two special right triangles determined by... measures Two special right triangles determined by... measures The sides of each Δ are always in a specific ratio... 5

6 Two special right triangles determined by... measures The sides of each Δ are always in a specific ratio... Your task is to figure out the side ratio for each Δ. Side length ratios for a --90 Δ

7 Side length ratios for a --90 Δ --90 Side length ratios for a --90 Δ

8 Side length ratios for a --90 Δ --90 Side length ratios for a --90 Δ

9 Side length ratios for a --90 Δ --90 Side length ratios for a --90 Δ

10 Side length ratios for a --90 Δ --90 a = Side length ratios for a --90 Δ --90 a = b = 0

11 Side length ratios for a --90 Δ --90 a = b = c = Side length ratios for a --90 Δ --90 a = b = c = c 2 = a 2 + b 2

12 Side length ratios for a --90 Δ --90 a = c = c 2 = a 2 + b 2 c 2 = b = Side length ratios for a --90 Δ --90 a = c = c 2 = a 2 + b 2 c 2 = c 2 = 2 b = 2

13 Side length ratios for a --90 Δ --90 a = c = c 2 = a 2 + b 2 c 2 = c 2 = 2 b = c = 2 Side length ratios for a --90 Δ --90 a = c = 2 b = c 2 = a 2 + b 2 c 2 = c 2 = 2 c = 2 3

14 Thm 7-8: --90 Δ --90 hyp = 2 * leg s s 2 s Side length ratios for a --90 Δ

15 Side length ratios for a --90 Δ --90 Side length ratios for a --90 Δ

16 Side length ratios for a --90 Δ --90 Side length ratios for a --90 Δ

17 Side length ratios for a --90 Δ --90 Is the --90 Δ / 2 of something Side length ratios for a --90 Δ --90 Is the --90 Δ / 2 of something 7

18 Side length ratios for a --90 Δ --90 Is the --90 Δ / 2 of something Side length ratios for a --90 Δ --90 Is the --90 Δ / 2 of something 8

19 Side length ratios for a --90 Δ --90 Is the --90 Δ / 2 of something Side length ratios for a --90 Δ --90 Is the --90 Δ / 2 of something equilateral Δ 9

20 Side length ratios for a --90 Δ Is the --90 Δ / 2 of something Side length ratios for a --90 Δ Is the --90 Δ / 2 of something 20

21 Side length ratios for a --90 Δ Is the --90 Δ / 2 of something Side length ratios for a --90 Δ Is the --90 Δ / 2 of something 2

22 Side length ratios for a --90 Δ --90 a = b = c = 2 Is the --90 Δ / 2 of something Side length ratios for a --90 Δ --90 a = b = c = 2 Is the --90 Δ / 2 of something c 2 = a 2 + b 2 22

23 Side length ratios for a --90 Δ --90 a = b = c = 2 Is the --90 Δ / 2 of something c 2 = a 2 + b = a Side length ratios for a --90 Δ --90 a = b = c = 2 Is the --90 Δ / 2 of something c 2 = a 2 + b = a = a

24 Side length ratios for a --90 Δ --90 a = b = c = 2 Is the --90 Δ / 2 of something c 2 = a 2 + b = a = a 2 + a 2 = 3 Side length ratios for a --90 Δ --90 a = b = c = 2 Is the --90 Δ / 2 of something c 2 = a 2 + b = a = a 2 + a 2 = 3 a = 3 24

25 Side length ratios for a --90 Δ --90 a = 3 c = 2 Is the --90 Δ / 2 of something b = c 2 = a 2 + b = a = a 2 + a 2 = 3 a = 3 Thm 7-9: --90 Δ --90 hyp = 2 * shorter leg s 3 2s longer leg = 3 * shorter leg s 25

26 The two special right triangles (Thm 7-8) (Thm 7-9) s s 2 s 3 2s s s Tips... Mental math is much faster than using a calculator. For these probs, answers almost always left in radical form. Do not leave a root/radical in the denominator of a fraction. First find shorter leg when working with a

27 Example Find length of the hypotenuse of a --90 Δ w/legs of length 5 6. Example 2 Find length of leg of a --90 Δ w/hypotenuse of length

28 Example 3 The distance from corner of a square playground to the opposite corner is 96ft. To the nearest foot, how long is each side of the playground Example 4 Find lengths of the legs of a --90 Δ w/hypotenuse of length

29 Example 5 The longer leg of a --90 has length 8. Find the lengths of the shorter leg and hypotenuse. Example 6 A garden shaped like a rhombus has a perimeter of 00ft & a... Find the area of the garden to the nearest foot. 29

30 L7-3 HW Problems Pg 369 #-29, 32, Pg 372 #-0