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?

Correct result:

F =  60.335 N


F1=42 N F2=35 N u=77+12/60=3865=77.2  x0=F1=42 y0=0 x=x0+F2 cosu=x0+F2 cos77.2 =42+35 cos77.2 =42+35 0.221548=49.7542 y=y0+F2 sinu=y0+F2 sin77.2 =0+35 sin77.2 =0+35 0.975149=34.13023 F=x2+y2=49.75422+34.13022=60.335 NF_{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 =x_{0} + F_{2} \cdot \ \cos 77.2^\circ \ =42 + 35 \cdot \ \cos 77.2^\circ \ =42 + 35 \cdot \ 0.221548=49.7542 \ \\ y=y_{0} + F_{2} \cdot \ \sin u ^\circ =y_{0} + F_{2} \cdot \ \sin 77.2^\circ \ =0 + 35 \cdot \ \sin 77.2^\circ \ =0 + 35 \cdot \ 0.975149=34.13023 \ \\ F=\sqrt{ x^2+y^2 }=\sqrt{ 49.7542^2+34.1302^2 }=60.335 \ \text{N}

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