To determine if the given values make a triangle, we need to check if the sum of the angles is equal to 180 degrees.
For the first set of values (86, 53, 51), let's find the sum of the angles:
86 + 53 + 51 = 190
Since the sum is not equal to 180 degrees, these values do not make a triangle.
For the second set of values (70, 22, 68):
70 + 22 + 68 = 160
Again, the sum is not equal to 180 degrees, so these values do not make a triangle.
For the third set of values (28, 64, 100):
28 + 64 + 100 = 192
Once again, the sum is not equal to 180 degrees, so these values do not make a triangle.
For the fourth set of values (47, 84, 56):
47 + 84 + 56 = 187
The sum is not equal to 180 degrees, so these values do not make a triangle.
For the fifth set of values (54, 97, 29):
54 + 97 + 29 = 180
Finally, we have a sum that is equal to 180 degrees. These values do make a triangle.
For the last set of values (33, 90, 57):
33 + 90 + 57 = 180
Once again, the sum is equal to 180 degrees, so these values make a triangle.
In summary:
- Set 1: Does not make a triangle
- Set 2: Does not make a triangle
- Set 3: Does not make a triangle
- Set 4: Does not make a triangle
- Set 5: Makes a triangle
- Set 6: Makes a triangle