(688,#5) Find the lengths of the sides of the triangle ABC[ A(2,1,0)

(688,#5) Find the lengths of the sides of the triangle ABC [ A(2,1,0), B(3,3,4), C(5,4,3) ] and determine whether the triangle is isosceles, a right triangle, both, or neither.
Solution:
Distance formula:

Two sides are not equal, therefore it is not an isosceles triangle.
By the law of cosines,

Applying this law :

Thus, is a right angle.

by:sh