Dot products and angle between cables

[musicmar]

Homework Statement

This is actually for an engineering class, but it's pretty basic vector addition.

Determine the angle θ between the two cables attached to the post.

I've attached the picture.

Homework Equations

The Attempt at a Solution

From the picture:
F₁:
α=?
β=?
γ= 35°

F₂:
α= 45°
β= 60°
γ= 120°

First, to find F₂, I used the angles and the formula cos(α)=(F_2x/F₂)

F₂=<282.84,200,-200>

To find F₁, I used the 35° from the vertical to find the z component, then used the 20° in the xy plane to find the x and y components.

F₁=<215.59,-78.47,327.66>


F₁·F₂=F₁F₂cosθ

θ=cos^-1(F₁·F₂/400²)
=cos^-1(-600.84/400²)=90.2°


According to the back of the book, the answer is 97.3°. So, I've made a mistake somewhere. Any help finding it would be greatly appreciated.

 

[gneill]

There's something funny going on with your angle calculation. Check your value for F1 dot F2. It should be in the neighborhood of -20,000 N².

 

[musicmar]

You're right. It was actually -20249 N^2. Thank you!