Question

A triangle is formed by the points A(1,0,0), B(3,2,0) and C(3,0,-2). What are the interior angles of this triangle?

Answer 1

All of the interior angles for this triangle are `60^o` (or `pi/3` radians)

Explanation:

`|AB| = sqrt((1-3)^2+(0-2)^2+(0-0)^2) = 2sqrt(2)`

`|BC| = sqrt((3-3)^2+(0-2)^2+(-2-0)^2) = 2sqrt(2)`

`|AC| = sqrt((3-1)^2+(0-0)^2+(-2-0)^2) = 2sqrt(2)`

Since all 3 sides are of equal length
the triangle is equilateral
and
all interior angles are `6o^o`