vector addition?

Question

5 paces east (0deg)
7 paces north east (45deg)
10 paces west (180deg)
7 paces north west (135deg)
I graphed it an the resultant is 117deg 11.5 paces
How do you add these vectors with the component method???

Answer 1

5(cos 0,sin 0) = 5(1,0) = (5,0)
7(cos 45,sin 45) = 7(1/√2,1/√2) = (4.95,4.95)
10(cos 180,sin 180) = 10(-1,0) = (-10,0)
7(cos 135,sin 135) = 7(-1/√2,1/√2) = (-4.95,4.95)
so add:
(5,0)
(4.95,4.95)
(-10,0)
(-4.95,4.95), getting
(-5, 9.90)
r² = (-5)² + 9.9² = 123.01
r = 11.09, not 11.5
tan Θ = 9.9/-5
Θ = 116.8°
your graph was close.