In the desert

A man wondering in the desert walks 5.7 miles in the direction S 26° W. He then turns 90° and walks 9 miles in the direction N 49° W. At that time, how far is he from his starting point, and what is his bearing from his starting point?

Correct answer:

m =  9.32 mi
φ =  274.8074 °

Step-by-step explanation:

a=5.7 mi b=9 mi  α=180+26=206  β=36049=311   x1=a sinα=a sin206° =5.7 sin206° =5.7 (0.438371)=2.49872 mi y1=a cosα=a cos206° =5.7 cos206° =5.7 (0.898794)=5.12313 mi  x2=b sinβ=b sin311° =9 sin311° =9 (0.75471)=6.79239 mi y2=b cosβ=b cos311° =9 cos311° =9 0.656059=5.90453 mi  x=x1+x2=(2.4987)+(6.7924)9.2911 mi y=y1+y2=(5.1231)+5.90450.7814 mi  m=x2+y2=(9.2911)2+0.78142=9.32 mi
tan φ = y:x x<0;y>0; . IV.Quadrant  Φ=π180°arctan(y/x)=π180°arctan(0.7814/(9.2911))4.8074   φ=270+Φ=270+4.8074=274.8074=274°4827"

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