Static Equilibrium of a tree sapling

AI Thread Summary
To stabilize the tree sapling, the sum of the forces must equal zero, leading to the equation involving vectors F_A, F_B, and F_C. Given F_A as 380 N and F_B as 260 N, the calculations for F_B's components yield 67.29 N for the vertical and 251.14 N for the horizontal. The equations for F_C's components are established, leading to the tangent calculation for the angle θ, which is found to be 51.23 degrees. The total angle between F_A and F_C is calculated to be 141.23 degrees, while the magnitude of F_C is computed as 401 N, though this value is questioned for accuracy. The discussion seeks further assistance to verify the calculations and resolve any discrepancies.
Bones
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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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