Answer:
B= 5626.77 m
C= 6220. 5 m
Explanation:
Because the sum of the vectors must be equal to zero, then the result force in x and the result force in y must be zero.
We propose 2 equations x-y to solve the problem:
Rx :resulting from forces at x
Ry: resulting from forces at y
Rx= Ax+Bx+Cx=0
Ry= Ay+By+Cy=0
Ax =1550 *cos25.6°= 1397.84
Ay =1550 *sin25.6° = 669.73
Bx= B*sin41° = 0.656B
By= -B*cos41° = -0.7547 B
Cx= -C*cos35.1°= -0.8181 C
Cy= C* sin35.1° = 0.575 C
Rx= 1397.84+0.656B-0.8181 C=0
Ry= 669.73-0.7547 B+ 0.575 C=0
System of 2 equations with 2 incognites:
+0.656B-0.8181 C= - 1397.84
-0.7547 B+ 0.575 C= -669.73
Resolving the system:
B= 5626.77 m
C= 6220. 5 m