The first step is to represent the vectors shown in the image in Cartesian coordinates.
For the vector C we have a magnitude of 4.8 and an angle 22 ° with the axis -y (direction j)
To write this vector in Cartesian coordinates we must find its component in x (address i) and in the y axis.
[tex]x = 4.8sin(22)i\\\\y = 4.8cos(22)(-j)[/tex]
So:
[tex]C = 4.8sin(22) i + 4.8cos(22)(-j)\\\\C = 1.798\ i - 4.450\ j[/tex]
For Vector B we have a magnitude of 5.6 and an angle of 33 with the -x axis (-i direction)
So:
[tex]x = 5.6cos(33)(-i)\\\\y = 5.6 sin(33)(-j)[/tex]
So:
[tex]B = 5.6cos(33)(-i) + 5.6sin(33)(-j)\\\\B = -4.696\ i - 3.05\ j[/tex]
Finally the sum of B + C is made component by component in the following way:
[tex]F = (-4.696 +1.798)i + (-4.450 - 3.05)j\\\\F = -2.898\ i - 7.5\ j[/tex]
Finally the magnitude of f is:
[tex]|F| = \sqrt{(-2,898)^2 + (-7.5)^2}[/tex]
| F | = 8.04
