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Unit 8 right triangles and trigonometry homework 2 Correct Responses;

  1. x = 13, y = 2·√13
  2. x = 15·√2 = y
  3. x = 6, y = 3·√3
  4. y = 17, x = 17·√3
  5. x = y = 10
  6. x = 50, y = 25
  7. x = 2·√7 = y
  8. x = 16·√3, y = 8·√3
  9. x = 11·√3, y = 33
  10. y = 2·√6, x = 3·√2
  11. x = √(10), y = 2·√5
  12. y = 8·√7, x = 4·√7
  13. x = 17·√3, z = 34·√3, y = 34·√6
  14. x = 18·√3, y = 18, z = 9
  15. x = 14·√2, y = 14, z = 14·√3
  16. x = 8·√3, y = 12·√2 = z
  17. z = 39·√2, x = 22·√3, y = 11·√3
  18. z = 10·√2, y = [tex]\dfrac{10 \cdot \sqrt{6} }{3}[/tex],  [tex]x= \dfrac{20 \cdot \sqrt{6} }{3}[/tex]
  19. y = 12, x = 6, z = 12·√2
  20. z = 10·√3, x = 20·√3, y = 30
  21. Perimeter = 24·√5
  22. Perimeter = 64·√2
  23. Length of the ramp = 6.25 feet
  24. Speed = 106.1 feet/s

Method by which the above responses are obtained;

1. An acute angle of the right triangle = 45°

Length of the legs are equal; x = 13

y = 2·√13

2. ∠45°

x = y

√2·x = 30

x = 30 ÷ √2 = 15·√2 = y

3. An acute angle of the right triangle = 60°

Therefore;

  • x = 3 × 2 = 6

6·√3 = 2·y

  • y = 3·√3

4. Interior angle = 30°

y = 34 ÷ 2 = 17

34·√3 = 2·x

x = 17·√3

5. Interior angle = 45°

x = y = 10

6. ∠60°

x·√3 = 2 × 25·√3

x = 50

y = 25

7. 45°

x·√2 = 2·√14

x = √2 × √14 = √28 = 2·√7 = y

8. ∠30°

x·√3 = 2 × 24

x = √3 × 2 × 8 = 16·√3

y = 8·√3

9. ∠60°

x = 11·√3

22·√3 × √3 = 2 × y

y = 33

10. ∠30°

y = 2·√6

2·√6 × √3 = 2·x

x = √(18) = 3·√2

11. ∠45°

x = √(10)

y = √(10)·√2 = √(20) = 2·√5

12. ∠60°

y·√3 = 2 × 4·√(21)

y = 8·√7

x = 4·√7

13. ∠30°

17·√3 = x

∠45°

Common side = 34·√3 = z

y = 34·√3 × √2 = 34·√6

14. ∠60°

x·√3 = 2 × 27

x = 2 × 9·√3 = 18·√3

Common side = 9·√3

y·√3 = 2 × 9·√3 = 18·√3

y = 18

z = 9

15. ∠45°

x = 14·√2

Common side = 28

∠30°

y = 14

28·√3 = 2×z

z = 14·√3

16. ∠30°

x = 8·√3

16·√3 × √3 = 2 × Common side

Common side = 24

∠45°

y·√2 = 24

y = 12·√2 = z

17. ∠45°

z = 39·√2

∠60°

x·√3 = 39 × 2

x = 22·√3

y = 11·√3

18. ∠45°

z·√2 = 20

z = 10·√2

y·√3 = 10·√2

y = 10·√2 ÷ √3 = 10·√6/3 = [tex]\dfrac{10 \cdot \sqrt{6} }{3}[/tex]

[tex]\underline{x= \dfrac{20 \cdot \sqrt{6} }{3}}[/tex]

19. ∠60°

a×√3 = 6·√3 × 2

a = 12 = y

x = 6

z = 12·√2

20. ∠45°

z·√2 = 10·√6

z = 10·√3

x = 20·√3

y×2 = 60

y = 30

21. ∠60°

s×√3 = 2 × 4·√15

Perimeter = 3 × 8 × √ 5 = 24·√5

22. ∠45°

s·√2 = 28

Perimeter = 4 × 14·√2 = 64·√2

23. Length of the ramp = 2 × 37.5 inches = 75 inches = 6.25 feet

24. Speed = 90·√2ft./(1.2 s) = 106.1 feet/s

Learn more about right triangles here:

https://brainly.com/question/2437195

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