Answer:
[tex]F = 62.93 [/tex]
[tex]\theta = 27.20^0[/tex]
Explanation:
Let us assume
east as positive
calculating the x components of each force:
F₁= 55 cos(45⁰)
= 38.89 N
F₂= 20 cos (30)
= 17.32 N
Y-components: (North is defined as positive)
F₁= 55 sin(45⁰)
= 38.89 N
F₂= -20 sin (30)
= -10 N
resultant force in x-direction = 38.89 + 17.32
= 56.21 N
resultant force in x-direction = 38.89 - 10
= 28.89 N
magnitude
[tex]F = \sqrt{56.21^2+28.89^2}[/tex]
[tex]F = 62.93 [/tex]
[tex]tan \theta = \dfrac{y}{x}[/tex]
[tex]tan \theta = \dfrac{28.89}{56.21}[/tex]
[tex]\theta = 27.20^0[/tex]
