MATH 122
NUMBER OF SOLUTIONS FOR A TRIANGLE
In each of the following, indicate the number of triangles that can be constructed with the given sides and angles.
Number of triangles |
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0 |
1 |
2 |
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| 1. | a = 45° | b = 6 | c = 5 | 1. |
x | ||
| 2. | a = 19° | b = 47° | c = 10 | 2. |
x | ||
| 3. | a = 76° | b = 42° | b = 6 | 3. |
x | ||
| 4. | a = 119° | b = 71° | b = 6 | 4. |
x | ||
| 5. | a = 2 | b = 2 | c = 4 | 5. |
x | ||
| 6. | a = 2 | b = 2 | c = 3 | 6. |
x | ||
| 7. | a = 10 | b = 6 | c = 12 | 7. |
x | ||
| 8 | a = 45° | b = 10 | a = 8 | 8. |
x | ||
| 9. | g = 45° | c = |
a = 10 | 9. |
x | ||
| 10. | b = 45° | c = 10 | b = 10 | 10. |
x | ||
| 11. | b = 45° | b = 12 | c = 10 | 11. |
x | ||
| 12. | b = 45° | b = 4 | c = 10 | 12. |
x | ||
| 13. | g = 130° | c = 10 | b = 5 | 13. |
x | ||
| 14. | g = 130° | c = 10 | a = 6 | 14. |
x | ||
| 15. | g = 130° | c = 5 | a = 6 | 15. |
x | ||
| 16. | g = 130° | c = 5 | a = 5 | 16. |
x | ||
| 17. | a = 60° | b = 14 | a = |
17. |
x | ||
| 18. | a = 60° | b = 14 | a = |
18. |
x | ||
| 19. | a = 60° | b = 14 | a = |
19. |
x | ||
| 20. | a = 60° | b = 14 | a = |
20. |
x | ||
21. How many triangles can be constructed with the following angles:
a = 100° b = 30.5° g = 50.5° ?
22. How many triangles can be constructed with the following angles:
a = 70.3° b = 43.5° g = 66.2° ?
answers: 21. none 22. many