Find the resultant of the vectors A, B, and C

Question

Vector A has magnitude 58 units and is inclined to the positive axis of x at 42 degrees. Vector B has magnitude 36 units and is inclined to the positive axis of x at 121 degrees. Vector C has magnitude 40 units and is inclined to the positive axis of x at 53 degrees. Find the resultant of vectors A, B, and C. 

Answer 1

Resolving each vector into x an y components
A= 58, B = 36 and C =40 units

Ax =A cos 42
Bx = - B Cos 59 ( as this acts in –ve X direction )  as  180- 121 = 59 
Cx = C Cos 53
Now Y components
Ay =A Sin 42
By = B Sin 59
Cy = C Sin 53
Net X component = Ax + Bx +Cx = 58 Cos 42 - 36 Cos 59 + 40 Cos 53 = Rx

( Here 59 has come as 180 -121 = 59 is in – X direction)

Net Y component = Ay +By +Cy = 58 Sin 42 + 36 Sin 59 + 40 Sin 53 =Ry
Hence the resultant
R = ( Rx² +Ry²)^1/2