(688,#7) Find the lengths of the sides of the triangle ABC {A(-2,6,1) B(5,4,-3),C(2,-6,4)} and determine whether the triangle is isosceles, a right triangle, both, or neither.

Solution:

Distance formula:

2 sides are not equal, therefore the triangle is not isosceles.

By the law of cosines,

Applying this law:

Thus is not a right angle, it is obtuse, greater than Pi/2. Consequently neither of the other two angles can be a right angle.

by:sh