Answer
magnitude of second vector is 871 and it makes angle of 36.019 degrees to the positive x-axis
Solution
In this question we have given
vector 1= [tex](550cos160,550sin160)[/tex]
and resultant =[tex](725cos75,725sin75)[/tex]
let second vector be V=[tex](Vcos\theta,Vsin\theta)[/tex]
[tex](550cos160,550sin160)+(Vcos\theta,Vsin\theta)=(725cos75,725sin75)[/tex]
[tex](-516.830, 188.1)+(Vcos\theta, Vsin\theta) = (187.64, 700.29)[/tex]
[tex](Vcos\theta, Vsin\theta) = (187.64, 700.29)-(-516.830, 188.1)\\(Vcos\theta, Vsin\theta)=(704.47,512.19)[/tex]............(1)
on comparing x and y component of both sides of equation 1
[tex]VCos\theta=704.47............(2)\\Vsin\theta=512.19[/tex]............(3)
Therefore,
divide equation 3 by equation (2)
[tex]\frac{Sin\theta}{cos\theta} Sin\theta=\frac{512.19}{704.47} \\tan\theta=.727\\\theta=36.019[/tex]
put value of [tex]\theta[/tex] in equation (2)
[tex]Vcos36.019=704.47\\V\times .8088=704.47\\V=871.0[/tex]
