Final answer:
The first set of side lengths forms an obtuse triangle, while the second set of side lengths forms a right triangle.
Step-by-step explanation:
To determine if the given side lengths form an acute, obtuse, or right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Let's calculate:
For the first set of side lengths (5.5, 5.8, 3.6):
5.5^2 + 5.8^2 = 30.25 + 33.64
= 63.89
3.6^2 = 12.96
Since 63.89 is greater than 12.96, the square of the hypotenuse is greater than the sum of the squares of the other two sides. Therefore, this triangle is obtuse.
For the second set of side lengths (50, 30, 1215, 19, 14):
50^2 + 30^2 = 2500 + 900
= 3400
1215^2 = 1476225
19^2 + 14^2 = 361 + 196 = 557
Since 3400 is equal to 1476225 + 557, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, this triangle is a right triangle.