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Sagot :
The special triangles have sin(60°) = cos(30°) = [tex]\frac{\sqrt{3} }{2}[/tex], and sin(30°) =
cos(60°) = 0.5, from which we have;
- x = 13, y = 13·√2
- x = 15·√2, y = 15·√2
- x = 6, y = 3·√3
- x = 17·√(3), y = 17
- x = y = 10
- x = 50, y = 25
- x = 2·√7, y = 2·√7
- x = 16·√3, y = 8·√3
- x = 11·√3, y = 33
- x = 3·√2, y = 2·√6
- x = √(10), y = 2·√(10)
- y = 8·√7, x = 4·√7
- x = 17·√3, y = 34·√2, z = 34,
- x = 18·√3, y = 18, z = 9
- x = 14·√2, y = 14, z = 14·√3
- x = 8·√3, y = z, = 12·√2
- x = 26·√3, y = 13·√3, z = 39·√2
- x = [tex]6\frac{2}{3} \cdot \sqrt{3}[/tex], y = [tex]3\frac{1}{3} \cdot \sqrt{3}[/tex], z = 10·√2
- x = 6, y = 12, z = 12·√2
- x = 20·√3, y = 30, z = 10·√3
- Perimeter = 24·√5
- Perimeter = 56·√2
- Length of he ramp = 75 inches
- The speed of the ball 75·√2 feet/s
Which method is used to solve special triangles?
The measures of the sides are;
1. x = 13, y = 13·√2
2. x = y, and x·√2 = 30
Which gives;
x = 15·√2, y = 15·√2
3. x = 3 ÷ 0.5 = 6, y = 3·√3
4. y = 34 × 0.5 = 17, x = 17·√(3)
5. x = y = 10
6. x = 50, y = 25
7. x·√2 = 2·√(14), which gives;
x = 2·√(14) ÷ √2 = √(28) = 2·√7 = y
x = 2·√7, y = 2·√7
8. x = 24 × 2 ÷ √3 = 16·√3
y = 8·√3
9. x = 11·√3, y = 33
10. y = 2·√6, x = 3·√2
11. x = √(10), y = 2·√(10)
12. y = 4·√(21) × 2 ÷ √3 = 8·√7
x = 4·√7
13. x = 17 ÷ tan(30°) = 17·√3
Common side = 34 = z
y = 34·√2
14. x = 27 × 2 ÷ √3 = 54·√3 ÷ 3 = 18·√3
Common side = 9·√3
y = 9·√3 × 2 ÷ √3 = 18
z = 9
15. x = 14·√2
Common side = 28
y = 14, z = 14·√3
16. x = 8·√3
Common side = 24
y·√2 = 24
Therefore;
y = 12·√2 = z
17. Common side = 39
x = 39 × 2 ÷ √3 = 26·√3
y = 13·√3
z = 39·√2
18. z = 10·√2 = The common side
x = 10·√2 × 2 ÷ √3 = 20·√6 ÷ 3
x = [tex]\underline{6\frac{2}{3} \cdot \sqrt{3}}[/tex]
y = [tex]\underline{3\frac{1}{3} \cdot \sqrt{3}}[/tex]
19. The common side = 12 = y
x = 6, z = 12·√2
20. z = 10·√3, x = 20·√3, y = 30
21. The perimeter = 3 × 8·√(5) = 24·√5
22. The perimeter = 4 × 14·√2 = 56·√2
23. The length of the ramp = 2 × 37.5 inches = 75 inches
24. Distance from the first base to the third base = 90·√2 feet
[tex]Speed = \dfrac{90 \cdot \sqrt{2} }{1.2} = 75 \cdot \sqrt{2}[/tex]
The speed of the ball 75·√2 feet/s
Learn more about special right triangles in here:
https://brainly.com/question/12237712
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