Thread: A triangle has vertices A (4,2,1), B (1,2,4), C (-1, 0, -4)

Use dot products to find all three angles of the triangle.

I already found the lengths of the three sides of the triangle: AB = 3sqrt(2), AC = 3sqrt(6) and BC = 6sqrt(2) and I already know the answers because I found them using trigonometry, but not sure how to do it using dot products.

To get the angles using dot product, you need the vectors, not the lengths.

Find:

the dot product of and to get the angle BAC.

the dot product of and to get the angle ABC.

the dot product of and to get the angle ACB.

Could you please give the first one as an example? I already know AB is <-3, 0, 3> and AC is <-5,-2,-5> (that is AB and AC with the arrow on top)

You will need the formula:



Applying this, we get:



There theta1 is the angle A.

Doing the dot product, we get:





theta1 is 90 degrees.

Thanks a lot, I really appreciate your help