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resultant force

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Knowing that $P_1=\\var{P1}$kN,  $P_2=\\var{P2}$kN  and  $P_3=\\var{P3}$kN,

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(a) Build a table with the force components, for example $P_{2x}=P_2 \\cos 20^\\circ$, $P_{2y}=P_2 \\sin 20^\\circ$, paying attention to the direction of a component:

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\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, kN y-component, kN $P_1=\\var{P1}\\text{kN}$ {comp[0][0]} {comp[0][1]} $P_2=\\var{P2}\\text{kN}$ {comp[1][0]} {comp[1][1]} $P_3=\\var{P3}\\text{kN}$ {comp[2][0]} {comp[2][1]}
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(b) Sum up the $x$-components $R_x=\\sum P_x$ and $y$-components $R_y=\\sum P_y$

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$R_x=\\var{comp[0][0]}+\\var{comp[1][0]}+\\var{comp[2][0]}=\\var{rx}\\text{kN}$

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$R_y=\\var{comp[0][1]}+\\var{comp[1][1]}\\simplify{+{comp[2][1]}}=\\var{ry}\\text{kN}$

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(c) The resultant is $R=\\sqrt{R_x^2+R_y^2}=\\sqrt{(\\var{rx})^2+(\\var{ry})^2}=\\var{r}\\text{kN}$

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(d) The angle with the horizontal is $\\alpha=\\arctan \\dfrac{R_y}{R_x}=\\arctan \\dfrac{\\var{ry}}{\\var{rx}}=\\var{a}^\\circ$

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$\\alpha=\\var{a}^\\circ$  $\\quad \\blacktriangleleft$

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Determine the $x$ and $y$ components of each of the forces shown.

\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, kN y-Component, kN {P1} kN [[0]] [[1]] {P2} kN [[2]] [[3]] {P3} kN [[4]] [[5]]
\n

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Determine the $x$ and $y$ components of the resultant force.

\n\n\n\n\n\n\n\n\n\n\n\n
 x-Component, kN y-Component, kN [[0]] [[1]]
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Determine the magnitude of the resultant force, kN.

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Determine the angle (in degrees) that the resultant force forms with axis $x$. Submit a positive angle if resultant force points up  or negative if down  from the $x$ axis.

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