Bearing

A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.

Correct answer:

s =  148.6607 km

Step-by-step explanation:

A=63+20/60=1903≐63.3333∘ B=153+20/60=4603≐153.3333∘ x1=50⋅ cos⁡A∘=50⋅ cos⁡63.3333333333∘ =50⋅ 0.448799=22.43996 km y1=50⋅ sin⁡A∘=50⋅ sin⁡63.3333333333∘ =50⋅ 0.893633=44.68163 km x2=140⋅ cos⁡B∘=140⋅ cos⁡153.333333333∘ =140⋅ (−0.893633)=−125.10857=(−229422π/5761) km y2=140⋅ sin⁡B∘=140⋅ sin⁡153.333333333∘ =140⋅ 0.448799=62.83189 km x=x1+x2=22.44+(−125.1086)≐−102.6686 km y=y1+y2=44.6816+62.8319≐107.5135 km s=x2+y2=(−102.6686)2+107.51352=10 221=148.6607 km

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