Question

The vertices of a triangle are given as (-4, 0, 0), (0, 0, 0), and (1, 5, 6). Determine whether the triangle is an acute triangle, an obtuse triangle, or a right triangle?

1) Acute triangle
2) Obtuse triangle
3) Right triangle

Answer 1

To determine the classification of the triangle, we need to find the measures of the angles. However, in this case, the measure of angle A is undefined, so we cannot classify the triangle as acute, obtuse, or right.

Step-by-step explanation:

To determine whether the triangle is acute, obtuse, or right, we need to find the measures of each angle and check their values. We can use the distance formula to find the lengths of the sides:

• d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
• AB = sqrt((-4 - 0)^2 + (0 - 0)^2 + (0 - 0)^2) = 4
• BC = sqrt((0 - 0)^2 + (0 - 0)^2 + (0 - 0)^2) = 0
• AC = sqrt((1 - (-4))^2 + (5 - 0)^2 + (6 - 0)^2) = sqrt(9 + 25 + 36) = sqrt(70)

Next, we can find the measures of the angles using the law of cosines:

• cos(A) = (BC^2 + AC^2 - AB^2) / (2 * BC * AC)
• cos(A) = (0^2 + sqrt(70)^2 - 4^2) / (2 * 0 * sqrt(70))
• cos(A) = (70 - 16) / 0 = undefined

Since the cosine of angle A is undefined, we cannot determine its measure and therefore cannot classify the triangle as acute, obtuse, or right.