Two forces

The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.

Correct result:

F =  1053.418 N

Solution:

F1=580 N F2=630 N A=0 ∘ B=59 ∘  x=F1⋅ cos⁡A∘+F2⋅ cos⁡B∘=F1⋅ cos⁡0∘ +F2⋅ cos⁡0∘ =580⋅ cos⁡0∘ +630⋅ cos⁡0∘ =580⋅ 1+630⋅ 1=904.47399 y=F1⋅ sin⁡A∘+F2⋅ sin⁡B∘=F1⋅ sin⁡0∘ +F2⋅ sin⁡0∘ =580⋅ sin⁡0∘ +630⋅ sin⁡0∘ =580⋅ 0+630⋅ 0=540.0154 F=x2+y2=904.4742+540.01542=1053.418 NF_{1}=580 \ \text{N} \ \\ F_{2}=630 \ \text{N} \ \\ A=0 \ ^\circ \ \\ B=59 \ ^\circ \ \\ \ \\ x=F_{1} \cdot \ \cos A ^\circ + F_{2} \cdot \ \cos B ^\circ =F_{1} \cdot \ \cos 0^\circ \ + F_{2} \cdot \ \cos 0^\circ \ =580 \cdot \ \cos 0^\circ \ + 630 \cdot \ \cos 0^\circ \ =580 \cdot \ 1 + 630 \cdot \ 1=904.47399 \ \\ y=F_{1} \cdot \ \sin A ^\circ + F_{2} \cdot \ \sin B ^\circ =F_{1} \cdot \ \sin 0^\circ \ + F_{2} \cdot \ \sin 0^\circ \ =580 \cdot \ \sin 0^\circ \ + 630 \cdot \ \sin 0^\circ \ =580 \cdot \ 0 + 630 \cdot \ 0=540.0154 \ \\ F=\sqrt{ x^2+y^2 }=\sqrt{ 904.474^2+540.0154^2 }=1053.418 \ \text{N}

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Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
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.
See also our trigonometric triangle calculator.

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