Answer to Question #198664 in Trigonometry for jessica

Question #198664

 Vector has magnitude of 20 km with quadrant bearing S 30° W and vector has magnitude of 35 km with quadrant bearing N 67°W. 




1
Expert's answer
2021-05-27T18:04:34-0400
SolutionSolution

The angle between y-axis and 12N12N Vectors is ; Therefore

     360 280=80Angle between vectors    θ=80+65=θ=145Then using a parallelogramAngle between vector      180θ    180145     35 Now, find the Resultant R=(12)2+(40)2+21240Cos(35)=2530.38596=50.30Direction(Use Sine)=Sin(35)Sin θ=R40Sin θ=40Sin(35)50.30θ=27.14\implies\ 360^\circ-\ 280^\circ\\ =80^\circ\\ Angle\ between\ vectors\\ \implies\theta=80+65\\ =\theta=145^\circ\\ Then\ using\ a\ parallelogram\\ Angle\ between\ vector\ \implies\ 180-\theta\\ \implies180-145\\ \implies\ 35^\circ\ Now,\ find\ the\ Resultant\ R\\ =\sqrt{(12)^2+(40)^2+2*12*40*Cos(35^\circ)}\\ =\sqrt{2530.38596}\\ =50.30\\ Direction(Use\ Sine)\\ =\frac{Sin(35^\circ)}{Sin\ \theta}=\frac{R}{40}\\ Sin\ \theta=\frac{40*Sin(35^\circ)}{50.30^\circ}\\ \theta=27.14^\circ


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