Question #346619

A plane leaves an airport with a bearing of S41W. After traveling 24 miles, the plane turns and travels on a bearing of N49W for 32 miles. At that time, what's the bearing of the plane from the airport?


1
Expert's answer
2022-06-01T02:54:30-0400

B=41°+49°=90°,\angle B=41\degree+49\degree=90\degree, so we have the right triangle ABC.

Let's find AC.

AC=AB2+CB2=242+322=1600=40.AC=\sqrt{AB^2+CB^2}=\sqrt{24^2+32^2}=\sqrt{1600}=40.

Now we can calculate A:\angle A:

sinA=BCAC=3240=0.8,sinA=\frac{BC}{AC}=\frac{32}{40}=0.8,

A53°.\angle A \approx53\degree.




So θ=180°(53°+41°)=86°.\theta=180\degree-(53\degree+41\degree)=86\degree.

 The bearing of the plane from the airport is N86W.


Answer: N86W.



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