Question

The route followed by a hiker consists of three displacement vectors , , and . Vector is along a measured trail and is 1710 m in a direction 40.0 ° north of east. Vector is not along a measured trail, but the hiker uses a compass and knows that the direction is 24.0 ° east of south. Similarly, the direction of vector is 43.0 ° north of west. The hiker ends up back where she started, so the resultant displacement is zero, or + + = 0. Find the magnitudes of (a) vector and (b) vector .

Currently stuck on 1693.27 but I'm missing a step.

(1309.62*0.6820)+(1093.94*0.7314)=1693.27

Answer 1

1710*cos40°+b*sin 24°-c*cos 43° = 0
1710*sin40°+c*sin 43°-b*cos24° = 0
Two equations, two unknown quantities !!!
1710*0.766+0.407b-0.731c = 0
1710*0.643+0.682c-0.913b = 0
c = (1710*0.766+0.407b)/0.731

c = 1792+0.557b

Also,

1099.5+0.682(1792+0.557b)-0.913b

2321.6= 0.533b
b = 2321.6/0.533 = 4354.7 m
c = 1792+0.557*4354.7 = 4217.6 m

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