Question

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.)​

Answer 1

Answer:

First, we can find the length of the North vector from Naples to Elgin with the sine law:

First, we can find the length of the North vector from Naples to Elgin with the sine law:450/sin(90°) = x/sin(46°)

First, we can find the length of the North vector from Naples to Elgin with the sine law:450/sin(90°) = x/sin(46°)x = 450*sin(46)

First, we can find the length of the North vector from Naples to Elgin with the sine law:450/sin(90°) = x/sin(46°)x = 450*sin(46)Then, we can use the sine law again to find the angle between the W<->E vector and vector going from Elgin to Canton:

First, we can find the length of the North vector from Naples to Elgin with the sine law:450/sin(90°) = x/sin(46°)x = 450*sin(46)Then, we can use the sine law again to find the angle between the W<->E vector and vector going from Elgin to Canton:675/sin(90°) = 450*sin(46)/sin(θ)

First, we can find the length of the North vector from Naples to Elgin with the sine law:450/sin(90°) = x/sin(46°)x = 450*sin(46)Then, we can use the sine law again to find the angle between the W<->E vector and vector going from Elgin to Canton:675/sin(90°) = 450*sin(46)/sin(θ)θ = sin-1(450*sin(46)/675)

First, we can find the length of the North vector from Naples to Elgin with the sine law:450/sin(90°) = x/sin(46°)x = 450*sin(46)Then, we can use the sine law again to find the angle between the W<->E vector and vector going from Elgin to Canton:675/sin(90°) = 450*sin(46)/sin(θ)θ = sin-1(450*sin(46)/675)The bearing angle (clockwise from north) can be calculated by subtracting the above angle from the west bearing angle of 270°:

First, we can find the length of the North vector from Naples to Elgin with the sine law:450/sin(90°) = x/sin(46°)x = 450*sin(46)Then, we can use the sine law again to find the angle between the W<->E vector and vector going from Elgin to Canton:675/sin(90°) = 450*sin(46)/sin(θ)θ = sin-1(450*sin(46)/675)The bearing angle (clockwise from north) can be calculated by subtracting the above angle from the west bearing angle of 270°:θ' = 270 - sin-1(450*sin(46)/675)

First, we can find the length of the North vector from Naples to Elgin with the sine law:450/sin(90°) = x/sin(46°)x = 450*sin(46)Then, we can use the sine law again to find the angle between the W<->E vector and vector going from Elgin to Canton:675/sin(90°) = 450*sin(46)/sin(θ)θ = sin-1(450*sin(46)/675)The bearing angle (clockwise from north) can be calculated by subtracting the above angle from the west bearing angle of 270°:θ' = 270 - sin-1(450*sin(46)/675)θ' ~ 241°

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

QUESTION 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.)

ANSWER 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  !!!!