# Forces

In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N, and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2, and F3.

Correct result:

F =  28.5 N
α =  45.4 °
β =  75.8 °
γ =  48.1 °

#### Solution:

$\alpha =\mathrm{arccos}\left(\frac{20}{F}\right)=45.{4}^{\circ }$
$\beta =\mathrm{arccos}\left(\frac{7}{F}\right)=75.{8}^{\circ }$
$\gamma =\mathrm{arccos}\left(\frac{19}{F}\right)=48.{1}^{\circ }$

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