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resultant force

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\n

Knowing that $\\alpha=\\var{a}^\\circ$, determine

(a)

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 Force x-component, N y-component, N 100 N $100 \\cos \\var{a}^\\circ=\\var{x100}$ $-100 \\sin \\var{a}^\\circ=\\var{y100}$ 150 N $150 \\cos (\\var{a}^\\circ+30^\\circ)=\\var{x150}$ $-150 \\sin (\\var{a}^\\circ+30^\\circ)=\\var{y150}$ 200 N $-200 \\cos \\var{a}^\\circ=\\var{x200}$ $-200 \\sin \\var{a}^\\circ=\\var{y200}$
\n

\n

$\\mathbf{R}=(\\sum F_x )\\mathbf{i}+(\\sum F_y )\\mathbf{j}=\\var{rx}\\mathbf{i}\\var{ry}\\mathbf{j},\\;\\text{N}$

\n

$R=\\sqrt{(\\var{rx})^2+(\\var{ry})^2}=\\var{R}\\;\\text{N}\\quad\\blacktriangleleft$

\n

(b)

\n

$\\theta=\\arctan \\dfrac{R_y}{R_x}=\\arctan \\dfrac{\\var{ry}}{\\var{rx}}=\\var{beta}^\\circ$  $\\quad\\blacktriangleleft$

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the magnitude of the resultant of the three forces shown, N:

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its direction in $^\\circ$, with respect to the horizontal line

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