Two beetles vector problem: why is my magnitude wrong?

[gokugreene]

Hey guys, I need your help figuring out what I am doing wrong.

Two beetles run across flat sand, starting at the same point. Beetle 1 runs 0.5m due east, then 0.80m at 30 degrees north of due east. Beetle 2 also makes two runs; the first is 1.6m at 40 degrees east of due north. What must be (a) the magnitude and (b) the direction of its second run if it is to end up at the new location of beetle 1?

40 degrees east of due north = 50 degrees

vector A = 0.5m
vector B = 0.8m
vector C = 1.6m

A = .5i + 0j
B = (.8cos(30))i + (.8sin(30))j
C = (1.6cos(50))i + (1.6sin(50))j

R = 2.35i + 1.78j
R = [2.35^2 + 1.78^2]^1/2 = 2.95m
arctan=(1.78/2.35)=37.14 degrees

Answer should be: (a) 0.84m (b) 79 degrees

What am I doing wrong here? Am I approaching it wrong?

 

[HallsofIvy]

You aren't showing the crucial part of your work! What did you do with vectors A, B, and C after you got them?

The first beetle's total motion is A+ B, then second's is C so to arrive at the same place the second beetle must go A+B- C.

 

[gokugreene]

I was adding A + B + C. I see how logically that wouldn't make sense. Thanks I got the answer.