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A helicopter flies from the airport on a course with a bearing of 21 degrees. After flying for 99 ​miles, the helicopter flies due east for some time. The helicopter flies back to the airport with a bearing of 227 degrees. How far did the helicopter fly on the final leg of its​ journey?

Answer :

okpalawalter8

Answer:

Step-by-step explanation:

From the question we are told that:

Initial bearing [tex]\angle _1=21 \textdegree[/tex]

Initial distance [tex]d_1=99miles[/tex]

Final bearing [tex]\angle _2=227 \textdegree[/tex]

Let [tex]\triangle OAB[/tex] be the perimeter travailed

[tex]\angle OAB=90+21=111 \textdegree\\\angle ABO=270-227=43 \textdegree[/tex]

 

Generally the equation for OB using sine rule is mathematically given by

[tex]OB=99*\frac{sin111}{sin43}[/tex]

[tex]OB=135.52miles[/tex]

Therefore the helicopter flight on the final leg of its​ journey is

[tex]OB=135.52miles[/tex]

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