Given two Vectors F1 and F2. where the magnitude of these vectors are F1= 59N and F2 =77N and where θ1=138degr

Question

Given two Vectors F1 and F2. where the magnitude of these vectors are F1= 59N and F2 =77N and where θ1=138degree and θ2= 264degree. the anngles are measure from the positive x-axis with counter-clockwise angular direction as positive.

1.) what is the magnitude of the resultant vector װFװ, where F=F1+F2. answer in units of N

2.) give the angle in degree, use counter-clockwise as the positive angular direction, between the limits of -180 degree and +180 degree from the positive x-axis. what is the direction of this resultant vectior F? answer in degree

plese help i'm lost

Answer 1

first find vertical movement by doing sin. do 59sin138+77sin264, or -37.099
then find horizontal with cos. do 59cos138+77cos264, or -51.894. do Pythagorean theorem to get the resultant as 63.79N
tan=opp/adj, so do arctan-37.099/-51.894 or 35.56 degrees, but you know its in the 3rd quadrant, so add 180 degrees to get 215.56, but then subtract 360 to make it a a negative angle to get -144.44 degrees. done!