sin 70 = Ay/75
Ay = 70.48 and that is positive ===> Ay = + 70.48
cos 70 = Ax/75
Ax = 25.65 and that is negative ===> Ax = - 25.65
B is in the 4th quadrant, 285 degrees counterclockwise from the + x axis (360 - 285 = 75 degrees clockwise from the +x axis. Because it is in the 4th quadrant x is positive and y is negative
We do the trig for a 15 - 75 - 90 triangle Hypotenuse is 125 units
sin 75 = By/125
By = 120.74 ====> - 120.74
cos 75 = Bx/125
Bx = 32.35 ===> + 32.35
Add the componets up:
Rx = -25.65 + 32 = 6.7
Ry = 70.48 - 120.74 = - 50.26
Rx + and Ry negative ===> Resultant is in the 4th quadrant
R^2 = Rx^2 + Ry^2
R^2 = 6.7^2 + (-50.26)^2 = 44.89 + 2526.07 = 2570.96
R = 50.70 (Magnatude)
Angle:
tan^-1 = Rx/Ry = 6.7/50.26 ( I already know final sign and quadrant, so I work with positive numbers until the end.
tan^-1 = 0.13331
angle = 7.59 degrees past the - y axis ===> angle = 270 + 7.59 = 277.59 degrees
QED