Consider the three distances .
Do they form a Pythagorean Triple?
Given A(5,2), B(-3,6), and C(1,-3), determine if triangle ABC is a right triangle.
So first I took a look at the angle between A and B:
cos theta = [5,2][-3,6] / magnitude of [5,2] x magnitude of [-3,6]
= -15 + 12 / square root of 25+4 x square root of 9+36
= -3 / square root of 1305
theta = about 85.2 degrees
Then I took a look at the angle between B and C:
cos theta = [-3,6][1,-3] / magnitude of [-3,6] x magnitude of [1,-3]
= -3 - 18 / square root of 9+36 x square root of 1+9
= -21 / square root of 450
theta = about 171.9 degrees
I didn't even calculate the angle between B and C, and i'm already over 180 degrees so where did I go wrong?
But the angle between A and B is 85.2 degrees + the angle between B and C is 171.9 degrees = 257.1 degrees
Am I missing something? 257.1 degrees is way over 180 degrees Don't I have to add all 3 angles? AB + BC + AC = 180 degrees.. So far I only calculated AB and BC and i'm at 257.1 degrees.