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# Math law of sines

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A plane flies 545 kilometers with a bearing of 316° from Naples to Elgin (see figure). The plane then flies 680 kilometers from Elgin to Canton (Canton is due west of Naples). Find the bearing of the flight from Elgin to Canton. (Round to the nearest whole number.)

Mar 16, 2021

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Let the angle formed by the triangle  at Canton =  C

And the angle formed  by the triangle at Naples =  90 - 44 = 46°

sin (46 ) /  680  =  sin C  / 545

545 * sin ( 46 )   /   680  =  sin C

arcsin ( 545 * sin (56)  /  680 )  = C  ≈  35.2°

Draw  a perpendicular from Elgin to the  base of  the triangle...call the point of intersection with  the  base, P

So let  the triangle   formed  by P , C   and  the angle formed by the perpendicular  at Elgin  be   PCE

So  angle   CEP  = 90   -   =  54.8°

This angle is  supplemental to 180

The suplemental angle is  125.2°

In terms of bearing, the  bearing  from Elgin to Canton = 360  -  125.2  = 234.8° ≈  235°

CORRECTED  !!!!

Mar 16, 2021
edited by CPhill  Mar 16, 2021
edited by CPhill  Mar 16, 2021
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the answer is wrong

far987  Mar 16, 2021
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Slight mistake....fix it in a sec

CPhill  Mar 16, 2021
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ok i will wait

far987  Mar 16, 2021
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I think it's correct, now....check me   !!!

CPhill  Mar 16, 2021
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far987  Mar 16, 2021
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Thank you this is a right answer how to give u check mark?

far987  Mar 17, 2021