Solving for Coordinate Angles in Statics Question

[RobertL]

Edit: Nevermind, it has been resolved.

Homework Statement

I have been attempting to solve what seems like a relatively pedestrian statics questions, but for some reason my answer is being marked as incorrect. The problem is as follows:

Determine the magnitude and coordinate direction angles of the resultant force acting at A. Given that F_B = 640N and F_C = 450N.

http://imgur.com/U3dSG

Homework Equations

N/A (no specific equations needed)

The Attempt at a Solution

I solved for the value of the resultant vector without any trouble by assigning point A as the origin and adding the components of the two original vectors. This gave me a value of 998.05=R. The resultant vector had the equation of 626.667i+13.33j+776.667k.

My attempt at solving for the coordinate angles ended in failure:

For example:
alpha=cos^-1(626.667/998.05)=51.1 degrees, which is incorrect.

Any thoughts would be greatly appreciated.

 

[jbsteele]

SolutionYou were using the wrong formula to calculate the coordinate angles. The correct formula is: θ = cos-1(x/R) where x is the component of the vector in the direction of the angle you are trying to find and R is the magnitude of the resultant vector. Using this formula, you can calculate the other two angles. The magnitude of the resultant vector is R = 998.05N and the components are 626.667i + 13.33j + 776.667k. For alpha, x=626.667 and for beta, x=13.33. Therefore, α = cos-1(626.667/998.05) = 51.20 degrees β = cos-1(13.33/998.05) = 8.43 degrees