Answer:
[tex]F_1+F_2= (28.26, 9.05) N[/tex]
[tex]\alpha = 17.7\º[/tex]
[tex]F = 29.67 N[/tex]
Explanation:
Hi!
In a (x, y) coordinate representation, the two forces are:
[tex]F_1=(12.7N, 0)\\F_2=(18.1N\cos(30\º), 18.1N \sin(30\º) )\\\cos(\º30)=0.86\\\sin(\º30)= 0.5[/tex]
The sum of the two forces is:
[tex]F_1 + F_2 = ( 12.7 + 0.86*18.1, 18.1*0.5) N[/tex]
[tex]F_1+F_2= (28.26, 9.05) N[/tex]
The angle to x-axis is calculated using arctan:
[tex]\alpha = \arctan(\frac{F_y}{F_x}) = \arctan(\frac{9.05}{28.26} = 17.7\º[/tex]
The magnitude is:
[tex]F = \sqrt {F_x^2 + F_y^2}= \sqrt{798.6 + 81.9} = 29.67 N[/tex]
