3. Revisit the sets of numbers in question 2. Which one would form a right triangle? Which one would form an acute triangle? Which one would form an obtuse triangle? Explain how you know.
From question 2:
Set A: {3, 4, 5}
This set would form a right triangle because it satisfies the Pythagorean Theorem which states that 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. In this case, 5^2 = 3^2 + 4^2, making it a right triangle.
Set B: {5, 6, 7}
This set would form an acute triangle because the sum of the squares of the two smaller sides is greater than the square of the longest side. In this case, 5^2 + 6^2 = 25 + 36 = 61, which is less than 7^2 = 49. Therefore, it would form an acute triangle.
Set C: {7, 8, 10}
This set would form an obtuse triangle because the square of the longest side is greater than the sum of the squares of the other two sides. In this case, 10^2 = 100, which is greater than 7^2 + 8^2 = 49 + 64 = 113. Therefore, it would form an obtuse triangle.