Answer :
Answer:
A= 61.35
B= -44.40
Explanation:
1. Using the components method we have:
[tex]A_{x}= A cos \alpha\\B_{x}= B cos \beta\\C_{x}= 0\\\\A_{y}= A sin \alpha\\B_{y}= B sin \beta\\C_{y}= 24.6\\[/tex]
Considering that the vector sum [tex]A+B+C=0[/tex], then:
[tex]|V|=\sqrt{V_{x}^{2} +V_{y}^{2} }=0[/tex]
Then:
[tex]V_{x} ^{2} =0; V_{x} =0\\V_{y} ^{2} =0; V_{y} =0[/tex]
It means the value of x and y component is 0.
2. Determinate the equations that describe each component:
[tex]V_{x}= A cos \alpha -B cos \beta=0 (1)\\V_{y}= A sin \alpha +B sin \beta - C=0 (2)[/tex]
Form Eq. (1):
[tex]A=B \frac{cos \beta}{cos \alpha} (3)[/tex]
Replacing A in Eq. (2):
[tex](B\frac{cos \beta}{cos \alpha})(sin \alpha)+ B sin\beta-C=0\\(B\frac{cos \beta}{cos \alpha})(sin \alpha)+ B sin\beta-=C\\\\B(\frac{cos \beta. sin \alpha}{cos \alpha}+ sin\beta)=C\\B=C(\frac{cos \beta. sin \alpha}{cos \alpha}+ sin\beta)^{-1} (4)[/tex]
Replacing values of C, α and β in (4):
[tex]B= 24.6 (\frac{(cos 27.7)(sin 44.9)}{cos 44.9}+sin 27.7)^{-1} \\B= -44.4[/tex]
Replacing value of B in (3)
[tex]A=-44.40\frac{cos 27.7}{sin 49.9} \\A= 61.35[/tex]