Question

The vertices of a triangle are given. Determine whether the triangle is an acute triangle, and obtuse triangle, or a right triangle. Explain your reasoning.

vertices: (2, -7, 3), (-1, 5, 8), (4, 6, -1)

Answer 1

The triangle is acute.

Step-by-step explanation:

To determine whether the triangle is acute, obtuse, or right, we can use the dot product of vectors. If the dot product is positive, the triangle is acute. If the dot product is negative, the triangle is obtuse. If the dot product is zero, the triangle is right.

Let's calculate the dot product:

(-1-2) + (5+7) + (8-3) = -3 + 12 + 5 = 14

Since the dot product is positive, the triangle is acute.