Answer:
The magnitudes of the second force is [tex]Z = 129.9 N[/tex]
The magnitudes of the resultant force is [tex]R = 256.047 N[/tex]
Explanation:
From the question we are told that
The force is [tex]F = 187 \ lb[/tex]
The angle made with second force [tex]\theta_o = 73 ^o 36' = 73 + \frac{36}{60} = 73.6^o[/tex]
The angle between the resultant force and the first force [tex]\theta _1 = 29 ^o 1 ' = 29 + \frac{1}{60} = 29.0167^o[/tex]
For us to solve problem we are going to assume that
The magnitude of the second force is Z N
The magnitude of the resultant force is R N
According to Sine rule
[tex]\frac{F}{sin (\theta _o - \theta_1 } = \frac{Z}{\theta _1}[/tex]
Substituting values
[tex]\frac{187}{sin(73.3 - 29.01667)} =\frac{Z}{sin (29.01667)}[/tex]
[tex]267.82 =\frac{Z}{0.4851}[/tex]
[tex]Z = 129.9 N[/tex]
According to cosine rule
[tex]R = \sqrt{F ^2 + Z^2 + 2(F) (Z) cos (\theta _o) }[/tex]
Substituting values
[tex]R = \sqrt{187^2 + 129.9 ^2 + 2 (187 ) (129.9) cos (73.6)}[/tex]
[tex]R = 256.047 N[/tex]