Finding the Obtuse Angle Between Diagonals in a Diagram

[masterofthewave124]

so i have to determine the obtuse angle between the diagonals in the following diagram:

http://img95.imageshack.us/img95/6112/obtuse9hg.jpg

this is what i have so far:

let's call the intersection of the diagonals O
so to find the obtuse angle, we can apply dot product (OW • OZ)

|OW| = 1/2 |YW|
= sqrt(61)/2

|OZ| = 1/2 |XZ|
= 3sqrt(24)/2

but if cos (theta) = (OW • OZ)/ (|OW||OZ|)

i don't have the numerator portion which is usually found with coordinates. so what do i do now?

 

[vsage]

Why not choose a coordinate system that is convenient?

 

[masterofthewave124]

oh ok so X = (0,0), W = (5,6), Z = (15,6), Y = (19,0)? and then go on to find the position vectors of OW and OZ?

 

[vsage]

You could do it that way. It doesn't really make a difference as long as you can construct vectors OW and OZ (using your logic)

 

[nrqed]

oh ok so X = (0,0), W = (5,6), Z = (15,6), Y = (19,0)? and then go on to find the position vectors of OW and OZ?

You mean Y = (10,0), right?

If you want the angle between the diagonals, then why not simply find the angle between the vectors (X,Z) and (Y,W)?

 

[masterofthewave124]

yeah the Y coordinate was a typo. and i can see how your method is easier as well. i think the technique i chose is a little bit better to visualize, as you can actually see the diagonals intersecting and forming the obtuse angle.