Find magnitude and direction of the resultant force?

Question

A force F1 of 12 newtons pulls due north. A force F2 of 5 newtons pulls due east. Find the magnitude and direction of the resultant force.

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Answer 1 · 2018-04-07T04:02:32

magnitude: $13$ $13$ Newtons

direction: $67.38$ $67.38$ degrees north of east

The Pythagorean Theorem can be used to find the magnitude of the resultant force of two forces that are perpendicular to each other:
magnitude:

$\sqrt{12^{2} + 5^{2}} =$ $sqrt(12^{2} + 5^{2}) =$
$\sqrt{144 + 25} =$ $sqrt(144 + 25) =$
$\sqrt{169} =$ $sqrt(169) =$
$13$ $13$ Newtons

Trigonometry can be used to find the direction of the resultant force:
direction:

$arctan (\frac{12}{5}) \approx$ $arctan(frac{12}{5}) approx$
$67.38$ $67.38$ degrees north of east