Question

The vertices of a triangle are given. Determine whether the triangle is an acute triangle, an obtuse triangle, or a right triangle. (-4, 0, 0), (0, 0, 0), (7, 2, 6)

Answer 1

Answer:

Obtuse triangle

Step-by-step explanation:

Given are the vertices of a triangle

Let A (-4, 0, 0),B (0, 0, 0),C(7, 2, 6)

Let us find angles between AB, BC and CA

AB = (4, 0,0): BC = (7,2,6) : CA = (11, 2,6)

Cos B = $\frac{AB.BC}{|AB||BC|}$

B = arc cos $\frac{AB.BC}{|AB||BC|}$=137 deg 54 min 7 sec

Similarly

A=29 deg 53 min 53 seconds

C = 12 deg 12 min 3 sec

Obtuse triangle since one angle > 90 degrees