The special triangles have sin(60°) = cos(30°) = , 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 = , y = , 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
<h3>Which method is used to solve special triangles?</h3>
The measures of the sides are;
1. x =<u> 13</u>, y =<u> 13·√2</u>
2. x = y, and x·√2 = 30
Which gives;
x = <u>15·√2</u>, y =<u> 15·√2</u>
3. x = 3 ÷ 0.5 =<u> 6</u>, y =<u> 3·√3</u>
4. y = 34 × 0.5 =<u> 17</u>, x =<u> 17·√(3)</u>
5. x = y =<u> 10</u>
6. x =<u> 50</u>, y =<u> 25</u>
7. x·√2 = 2·√(14), which gives;
x = 2·√(14) ÷ √2 = √(28) = 2·√7 = y
x = <u>2·√7</u>, y =<u> 2·√7</u>
8. x = 24 × 2 ÷ √3 =<u> 16·√3</u>
y =<u> 8·√3</u>
9. x =<u> 11·√3</u>, y =<u> 33</u>
10. y = 2·√6, x =<u> 3·√2</u>
11. x =<u> √(10)</u>, y =<u> 2·√(10)</u>
12. y = 4·√(21) × 2 ÷ √3 =<u> 8·√7</u>
x =<u> 4·√7</u>
13. x = 17 ÷ tan(30°) =<u> 17·√3</u>
Common side =<u> 34 </u>= z
y =<u> 34·√2</u>
14. x = 27 × 2 ÷ √3 = 54·√3 ÷ 3 =<u> 18·√3</u>
Common side = 9·√3
y = 9·√3 × 2 ÷ √3 =<u> 18</u>
z =<u> 9</u>
15. x =<u> 14·√2</u>
Common side = 28
y =<u> 14</u>, z =<u> 14·√3</u>
16. x =<u> 8·√3</u>
Common side = 24
y·√2 = 24
Therefore;
y = <u>12·√2 </u>= z
17. Common side = 39
x = 39 × 2 ÷ √3 =<u> 26·√3</u>
y =<u> 13·√3</u>
z =<u> 39·√2</u>
18. z =<u> 10·√2</u> = The common side
x = 10·√2 × 2 ÷ √3 = 20·√6 ÷ 3
x =
y =
19. The common side =<u> 12 </u>= y
x =<u> 6</u>, z =<u> 12·√2</u>
<u />
20. z =<u> 10·√3</u>, x = <u>20·√3</u>, y =<u> 30</u>
21. The perimeter = 3 × 8·√(5) = <u>24·√5</u>
22. The perimeter = 4 × 14·√2 =<u> 56·√2</u>
23. The length of the ramp = 2 × 37.5 inches =<u> 75 inches</u>
24. Distance from the first base to the third base = 90·√2 feet
The speed of the ball <u>75·√2 feet/s</u>
Learn more about special right triangles in here:
brainly.com/question/12237712