Help Sine cosine law magnitude and direction

[Xantheri]

FA and FB balances the metal beam with a 360N of weight. FB experiences a force of 200N while FA is oriented at 30° from the y-axis. Using SINE/COSINE LAW, solve fora) Magnitude of FAb) Direction of FB

 

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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.