To solve for the magnitude of FA using the sine law, we can set up the following equation:
sin(30°) / FA = sin(90°) / 360N
Simplifying this equation, we get:
FA = sin(30°) * 360N / sin(90°)
FA = 0.5 * 360N
FA = 180N
Therefore, the magnitude of FA is 180N.
To solve for the direction of FB using the cosine law, we can set up the following equation:
FB^2 = FA^2 + 200N^2 - 2 * FA * 200N * cos(30°)
Simplifying this equation, we get:
FB^2 = 180N^2 + 200N^2 - 2 * 180N * 200N * cos(30°)
FB^2 = 32400N^2
Taking the square root of both sides, we get:
FB = 180N
Therefore, the magnitude of FB is 180N.
To solve for the direction of FB, we can use the following equation:
tan(θ) = opposite / adjacent
tan(θ) = 200N / 180N
tan(θ) = 1.111...
θ = tan^-1(1.111...)
θ = 48.2° (rounded to one decimal place)
Therefore, the direction of FB is 48.2° from the y-axis.