Resultant Force Problem

[dear_miss_katie]

Hello. I need help with this problem in math. I have struggled with is and do not know where to start. If I could get a hint from anyone it would be of great help to me. Thank you! Here is the word problem:
Three forces with magnitudes of 75 lbs, 100 lbs, and 125 lbs act on an object at angles of 30 degrees, 45 degrees, 120 degrees, respectively, with the positive x-axis. Find the directio nand magnitude of the resultant of these forces.

I have tried to draw a picture alread....but I do know know if I have drawn correctly. Is the resultant the sum of all 3 of the forces?

 

[skeeter]

let vector A be the 75 lb force, B the 100 lb force, C the 125 lb force, and R the resultant force.

using the method of components ...

A[sub:17mf4tvf]x[/sub:17mf4tvf] + B[sub:17mf4tvf]x[/sub:17mf4tvf] + C[sub:17mf4tvf]x[/sub:17mf4tvf] = R[sub:17mf4tvf]x[/sub:17mf4tvf]

75cos(30) + 100cos(45) + 125cos(120) = R[sub:17mf4tvf]x[/sub:17mf4tvf]

A[sub:17mf4tvf]y[/sub:17mf4tvf] + B[sub:17mf4tvf]y[/sub:17mf4tvf] + C[sub:17mf4tvf]y[/sub:17mf4tvf] = R[sub:17mf4tvf]y[/sub:17mf4tvf]

75sin(30) + 100sin(45) + 125sin(120) = R[sub:17mf4tvf]y[/sub:17mf4tvf] edit ... fixed typo on the subscript

magnitude of the resultant vector is ...

\(\displaystyle |R| = \sqrt{R_x^2 + R_y^2}\)

since both R[sub:17mf4tvf]x[/sub:17mf4tvf] and R[sub:17mf4tvf]y[/sub:17mf4tvf] are positive, the direction of R is in quadrant I ...

\(\displaystyle \theta = \arctan \left(\frac{R_y}{R_x}\right)\)

hard part is done, now get out your calculator and determine the magnitude and direction of R.

 

[dear_miss_katie]

Oh, my goodness that was sooooooooooooooooo helpful!!!! Thank you, thank you! I totally didn't get it when the teacher explained it, but that makes perfect sense. My answer came out right this time . Thanks!