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Unit 8 right triangles and trigonometry homework 2 Correct Responses;
- x = 13, y = 2·√13
- x = 15·√2 = y
- x = 6, y = 3·√3
- y = 17, x = 17·√3
- x = y = 10
- x = 50, y = 25
- x = 2·√7 = y
- x = 16·√3, y = 8·√3
- x = 11·√3, y = 33
- y = 2·√6, x = 3·√2
- x = √(10), y = 2·√5
- y = 8·√7, x = 4·√7
- x = 17·√3, z = 34·√3, y = 34·√6
- x = 18·√3, y = 18, z = 9
- x = 14·√2, y = 14, z = 14·√3
- x = 8·√3, y = 12·√2 = z
- z = 39·√2, x = 22·√3, y = 11·√3
- z = 10·√2, y = [tex]\dfrac{10 \cdot \sqrt{6} }{3}[/tex], [tex]x= \dfrac{20 \cdot \sqrt{6} }{3}[/tex]
- y = 12, x = 6, z = 12·√2
- z = 10·√3, x = 20·√3, y = 30
- Perimeter = 24·√5
- Perimeter = 64·√2
- Length of the ramp = 6.25 feet
- 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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