# Resultant force

Calculate mathematically and graphically the resultant of a three forces with a common centre if:

F1 = 50 kN α1 = 30°
F2 = 40 kN α2 = 45°
F3 = 40 kN α3 = 25°

Correct result:

F =  113.1225 kN
f =  65.613 °

#### Solution:

$f=\frac{18{0}^{\circ }}{\pi }\cdot \mathrm{arctan}\left(y\mathrm{/}x\right)=\frac{18{0}^{\circ }}{\pi }\cdot \mathrm{arctan}\left(103.0293\mathrm{/}46.7081\right)=65.61{3}^{\circ }=6{5}^{\circ }3{6}^{\mathrm{\prime }}47\mathrm{"}$

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