# 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.

Result

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

#### Solution:

$F = \sqrt{ 20^2+ 7^2+ 19^2} = 28.5 \ \text { N }$
$\alpha = \arccos(\dfrac{ 20 }{F}) = 45.4 ^\circ$
$\beta = \arccos(\dfrac{ 7 }{F}) = 75.8 ^\circ$
$\gamma = \arccos(\dfrac{ 19 }{F}) = 48.1 ^\circ$

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#### Following knowledge from mathematics are needed to solve this word math problem:

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