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# Newtons

direction: #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(144 + 25) =#
#sqrt(169) =#
#13# Newtons

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

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