How Can I Solve for F and X Using Trigonometric Identities?

[fs93]

Homework Statement

I have resolved three vectors to get the final equations with two unknowns.

F [force]
X [Angle]

FcosX = 4.1
FsinX = 6.4

Homework Equations

The Attempt at a Solution

Here is what I tried to do but failed miserably.

sinX=6.4/F
X=arcsin(6.4/F)

cosX=4.1/F
X=arccos(4.1/F)

I tried to solve for X = X --- but then I have no idea how to solve for F.

 

[srmeier]

Homework Statement

I have resolved three vectors to get the final equations with two unknowns.

F [force]
X [Angle]

FcosX = 4.1
FsinX = 6.4

Homework Equations

The Attempt at a Solution

Here is what I tried to do but failed miserably.

sinX=6.4/F
X=arcsin(6.4/F)

cosX=4.1/F
X=arccos(4.1/F)

I tried to solve for X = X --- but then I have no idea how to solve for F.

Ok well, you solved for X in terms of F. To solve for F use the Pythagorean Theorem. (6.4) is one component of the force vector and (4.1) is the other component. Therefore, F=sqr((6.4)^2+(4.1)^2). We know that this is a valid step because we add vectors tip to tail (in this case creating a right angle).