- #1

- 100

- 0

## 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:

F

_{1}:

**α**=?

β=?

**γ**= 35°

F

_{2}:

**α**= 45°

β= 60°

**γ**= 120°

First, to find F

_{2}, I used the angles and the formula cos(

**α**)=(F

_{2x}/F

_{2})

F

_{2}=<282.84,200,-200>

To find F

_{1}, 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.

F

_{1}=<215.59,-78.47,327.66>

F

_{1}·F

_{2}=F

_{1}F

_{2}cosθ

θ=cos

^{-1}(F

_{1}·F

_{2}/400

^{2})

=cos

^{-1}(-600.84/400

^{2})=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.