does 86dgree, 58dgr, and 41dgr make a triangle?
In order to determine if three angles can make a triangle, we need to apply the triangle inequality theorem. According to this theorem, the sum of any two angles in a triangle must be greater than the measure of the third angle.
Let's check the three given angles:
86° + 58° = 144°
Since 144° is greater than 41°, the sum of the two larger angles is indeed greater than the smaller angle.
58° + 41° = 99°
Again, 99° is greater than 86°, so the sum of the two larger angles is greater than the smaller angle.
86° + 41° = 127°
Even here, 127° is greater than 58°, meaning the sum of the two larger angles is greater than the smaller angle.
Therefore, since all three pairs of angles satisfy the triangle inequality theorem, these angles can indeed form a triangle.
what about 47, 84, 56?
To determine if the lengths 47, 84, and 56 can form a triangle, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check the three given side lengths:
47 + 84 = 131
Since 131 is greater than 56, the sum of the two longer sides is indeed greater than the length of the third side.
84 + 56 = 140
Here, 140 is also greater than 47, meaning the sum of the two longer sides is greater than the length of the third side.
47 + 56 = 103
However, 103 is less than 84, so the sum of the two shorter sides is not greater than the length of the third side.
Therefore, these three side lengths, 47, 84, and 56, do not form a triangle.
70, 22, 68?
To determine if the lengths 70, 22, and 68 can form a triangle, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check the three given side lengths:
70 + 22 = 92
Since 92 is greater than 68, the sum of the two longer sides is indeed greater than the length of the third side.
70 + 68 = 138
Here, 138 is also greater than 22, meaning the sum of the two longer sides is greater than the length of the third side.
22 + 68 = 90
Since 90 is greater than 70, the sum of the two shorter sides is also greater than the length of the third side.
Therefore, these three side lengths, 70, 22, and 68, can form a triangle.
54, 97, 29?
To determine if the lengths 54, 97, and 29 can form a triangle, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check the three given side lengths:
54 + 97 = 151
Since 151 is greater than 29, the sum of the two longer sides is indeed greater than the length of the third side.
54 + 29 = 83
Here, 83 is also greater than 97, meaning the sum of the two shorter sides is greater than the length of the third side.
97 + 29 = 126
Since 126 is greater than 54, the sum of the two shorter sides is also greater than the length of the third side.
Therefore, these three side lengths, 54, 97, and 29, can form a triangle.
28, 64, 100?
To determine if the lengths 28, 64, and 100 can form a triangle, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check the three given side lengths:
28 + 64 = 92
Since 92 is less than 100, the sum of the two shorter sides is not greater than the length of the third side.
28 + 100 = 128
Here, 128 is greater than 64, meaning the sum of the two shorter sides is greater than the length of the third side.
64 + 100 = 164
Since 164 is greater than 28, the sum of the two longer sides is also greater than the length of the third side.
Therefore, these three side lengths, 28, 64, and 100, can form a triangle.