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VARVARA [1.3K]
3 years ago
12

Unit 8 right triangles and trigonometry homework 2 answers key.

SAT
1 answer:
OlgaM077 [116]3 years ago
5 0
<h3>Unit 8 right triangles and trigonometry homework 2 Correct Responses;</h3>
  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 = \dfrac{10 \cdot \sqrt{6} }{3},  x= \dfrac{20 \cdot \sqrt{6} }{3}
  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

<h3>Method by which the above responses are obtained;</h3>

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

Length of the legs are equal; x = 13

y = <u>2·√13</u>

2. ∠45°

x = y

√2·x = 30

x = 30 ÷ √2 =<u> 15·√2</u> = y

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

Therefore;

  • x = 3 × 2 =<u> 6</u>

6·√3 = 2·y

  • y =<u> 3·√3</u>

4. Interior angle = 30°

y = 34 ÷ 2 = 17

34·√3 = 2·x

x = <u>17·√3</u>

5. Interior angle = 45°

x = y =<u> 10</u>

6. ∠60°

x·√3 = 2 × 25·√3

x = <u>50</u>

y =<u> 25</u>

7. 45°

x·√2 = 2·√14

x = √2 × √14 = √28 =<u> 2·√7 </u>= y

8. ∠30°

x·√3 = 2 × 24

x = √3 × 2 × 8 =<u> 16·√3</u>

y = <u>8·√3</u>

9. ∠60°

x = <u>11·√3</u>

22·√3 × √3 = 2 × y

y =<u> 33</u>

10. ∠30°

y =<u> 2·√6</u>

2·√6 × √3 = 2·x

x = √(18) = <u>3·√2</u>

11. ∠45°

x = √(10)

y = √(10)·√2 = √(20) =<u> 2·√5</u>

12. ∠60°

y·√3 = 2 × 4·√(21)

y =<u> 8·√7</u>

x = <u>4·√7</u>

13. ∠30°

<u>17·√3 </u>= x

∠45°

Common side = <u>34·√3</u> = z

y = 34·√3 × √2 = <u>34·√6</u>

14. ∠60°

x·√3 = 2 × 27

x = 2 × 9·√3 = <u>18·√3</u>

Common side = 9·√3

y·√3 = 2 × 9·√3 = 18·√3

y = <u>18</u>

z = <u>9</u>

15. ∠45°

x = <u>14·√2</u>

Common side = 28

∠30°

y = <u>14</u>

28·√3 = 2×z

z = <u>14·√3</u>

16. ∠30°

x = <u>8·√3</u>

16·√3 × √3 = 2 × Common side

Common side = 24

∠45°

y·√2 = 24

<u>y = 12·√2 = z</u>

17. ∠45°

z = <u>39·√2</u>

∠60°

x·√3 = 39 × 2

x = <u>22·√3</u>

y =<u> 11·√3</u>

18. ∠45°

z·√2 = 20

z = <u>10·√2</u>

y·√3 = 10·√2

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

\underline{x= \dfrac{20 \cdot \sqrt{6} }{3}}

19. ∠60°

a×√3 = 6·√3 × 2

a =<u> 12 = y</u>

<u>x = 6</u>

<u>z = 12·√2</u>

20. ∠45°

z·√2 = 10·√6

<u>z = 10·√3</u>

<u>x = 20·√3</u>

y×2 = 60

<u>y = 30</u>

21. ∠60°

s×√3 = 2 × 4·√15

<u>Perimeter = 3 × 8 × √ 5 = 24·√5</u>

22. ∠45°

s·√2 = 28

<u>Perimeter = 4 × 14·√2 = </u>64·√2

23. Length of the ramp = 2 × 37.5 inches = 75 inches = <u>6.25 feet</u>

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

Learn more about right triangles here:

brainly.com/question/2437195

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