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.

Answer 1

Set A: 3, 4, 5
Set B: 4, 7, 9
Set C: 5, 12, 13

To form a right triangle, the Pythagorean theorem must be satisfied, which states that the sum of the squares of the two shorter sides equals the square of the longest side. For Set A, 3^2 + 4^2 = 5^2, therefore Set A forms a right triangle.

An acute triangle is a triangle where all angles are less than 90 degrees. To determine if a triangle is acute, we can use the Law of Cosines, which states that in a triangle with sides a, b, and c, and angles A, B, and C respectively, c^2 = a^2 + b^2 - 2ab * cos(C). If this is true for all sides, then the triangle is acute. For Set C, 5^2 = 12^2 + 13^2 - 2*12*13 * cos(C). Cos(C) > 0, which means that angle C is less than 90 degrees, therefore Set B forms an acute triangle.

An obtuse triangle is a triangle where one angle is greater than 90 degrees. For Set B, 4^2 = 7^2 + 9^2 - 2*7*9 * cos(B). Cos(B) < 0, which means that angle B is greater than 90 degrees, therefore Set B forms an obtuse triangle.