Static Equilibrium of a tree sapling

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SUMMARY

The discussion focuses on solving for the unknown force vector FC acting on a tree sapling subjected to two known forces, FA = 380 N and FB = 260 N. The equilibrium condition requires that the sum of the forces equals zero. The calculations provided lead to an angle θ = 51.23 degrees and an initial magnitude estimate of FC = 401 N, which the user questions for accuracy. The correct approach involves resolving the forces into their components and applying trigonometric identities to ensure equilibrium.

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Homework Statement



Three forces are applied to a tree sapling, as shown in the figure, to stabilize it. If vector F A = 380 N and vector F B = 260 N, find vector F C in magnitude and direction.
http://www.webassign.net/gianpse4/12-45.gif


Homework Equations





The Attempt at a Solution


I am not sure where to begin...Help!
 
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Hint : To stabilize the tree, the sum of the three forces must be 0N.
 
Fa=380N
Fbsin(15)=67.29

380N-67.29=fcsinθ
312.71N=Fcsinθ


Fbcos(15)=Fccosθ

Fbcos(15)= 251.14

so Fccosθ=251.14

we now know Fcsinθ and Fccosθ

tanθ=opp/adj

θ=arctan(312.71/251.14)= 51.23 degrees

so the angle Fa to Fc equals 51.23 degrees+ 90 degrees=141.23 degrees

the magnitude of Fc= √Fcx2+Fcy2

magnitude of Fc= 401N which doesn't seem to be correct...any help??
 

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