Saved Bookmarks
| 1. |
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» 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: Mark as BRAINLIEST if helpful. |
|