# Forces

Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?

Result

F =  60.335 N

#### Solution:

$F_{1}=42 \ \text{N} \ \\ F_{2}=35 \ \text{N} \ \\ u=77+12/60=\dfrac{ 386 }{ 5 }=77.2 \ ^\circ \ \\ x_{0}=F_{1}=42 \ \\ y_{0}=0 \ \\ x=x_{0} + F_{2} \cdot \ \cos( u ^\circ \rightarrow\ \text{rad})=x_{0} + F_{2} \cdot \ \cos( u ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=42 + 35 \cdot \ \cos( 77.2 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=49.7542 \ \\ y=y_{0} + F_{2} \cdot \ \sin( u ^\circ \rightarrow\ \text{rad})=y_{0} + F_{2} \cdot \ \sin( u ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=0 + 35 \cdot \ \sin( 77.2 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=34.13023 \ \\ F=\sqrt{ x^2+y^2 }=\sqrt{ 49.7542^2+34.1302^2 } \doteq 60.3353 \doteq 60.335 \ \text{N}$

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Tips to related online calculators
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
Pythagorean theorem is the base for the right triangle calculator.

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