2 unknown Forces+known resultant force

AI Thread Summary
The discussion revolves around calculating the forces Fa and Fb acting on an object being pulled with a known resultant force of 970 N along the x-axis. The angles for Fa and Fb are given as 20 degrees and 51 degrees, respectively. The user attempts to apply the law of sines and cosines to solve the problem but encounters difficulties, resulting in unexpectedly small values for the forces. They seek clarification on how to correctly express the x components of Fa and Fb. The conversation highlights the importance of correctly applying vector resolution techniques in mechanics.
Xiomara

Homework Statement


Hi, I'm having trouble with my first mechanics assignment and I'd appreciate some help.
So, an object is being pulled using two ropes (Fa and Fb) with a resultant force of 970 N along the x axis. The angle from Fa to the axis is 20 degrees, angle from fb to the axis is 51 degrees. I need to calculate Fa and Fb.

Homework Equations


I think that I need to use either law of sines or cosines but am not sure.
c^2=a^2+b^2-2abcos(c)
sin(A)/a=sin(B)/b=sin(C)/c

The Attempt at a Solution


I made a vector diagram (triangle). I then tried to find F a and b by plugging all my knowns into the law of sines and solving. sin(C)/c=sin(51)/970=8.0118, but when I try to calculate the others based on this I get very small numbers, less than one. What am I doing wrong??
 
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How would you write the x component of ##F_{a}## and ##F_{b}##?
 

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