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Posted on Dec 19, 2008

Trig and distance

A pilot flies a plane north for 300 kilometers then 80 degrees east for 100 kilometers, find the distance from the starting point and direction

  • gnagner Apr 08, 2009

    How do you solve for θ in (1/3)= cos² (θ/2)?

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  • Posted on Dec 19, 2008
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Debs,

this is solved by starting with the SECOND leg of the flight considered as a triangle.

Find how far DUE east the plane travels (100 km x Cos10 = 83.9 km) using 10 degrees because that is how much is left of the 90 degree quadrent after subtracting the 80 degrres course direction.
Similarly find out how far DUE north the plane travels (100 km x Cos80 = 11 km).

Now get the total flight NORTH = 300 + 11 = 311
- and total EAST = 83.9

Finally, use Pythagoras theorem.to get the total DISTANCE:
square root of ( 311 squared + 83 squared ) = 321 km

Also the DIRECTION from its Tangent of 83 /311 = 14.9 degrees



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v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} w\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} Normal 0 false false false MicrosoftInternetExplorer4 st1\:*{behavior:url(#ieooui) } /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman"; mso-ansi-language:#0400; mso-fareast-language:#0400; mso-bidi-language:#0400;} It’s hard to cover all the details in a forum like this but I’ll give you a quick primer. I can send you a powerpoint presentation that explains it in a little more detail. To really learn how to read latitude and longitude you should pick up a copy of “Chapman’s Piloting and Seamanship.”

The earth is divided into parallels of latitude and meridians of longitude, also known as lines of position.

clip_image002.jpg

Latitude is measured north and south of the equator, with the equator represented as 0 degrees, and the poles being represented as 90 degrees North or South. Latitude lines are paralel to the equator. For example, if I was at the equator I would be at 0 degrees. If I traveled exactly 60 nautical miles to the north, I would be at 1 degree North, and if I traveled another 60 miles I would be at 2 degrees north. Your GPS display will preface the Latitude measurement with an “N” for positions North of the equator and an “S” for positions south of the equator.

Longitude measures your position east or west from the Prime Meridian, which is a line represented as 0 degrees that bisects the earth from north to south and passes through Greenwich England. Halfway around the earth at the International Dateline Longitude is 180 degrees. Measuring Longitude is a little more complicated because the lines are not parallel and requires an accurate clock (your GPS) to compare time at your location relative to the time in Greenwich England. Your GPS display will preface the Longitude measurement with a “W” for positions west of Greenwich and an “E” for positions east of Greenwich.

To make more accurate measurements each degree is divided into 60 minutes. Because the lines are parallel, 1 minute of latitude is equal to 1 nautical mile. Each minute can be further divided into 60 seconds. Each second is roughly equivalent to a distance of 100’ Instead of seconds, the default setting on your Garmin breaks the minute down into tenths, hundredths, and thousandths for meven more precise measurements. Because they are not parallel, lines of Longitude are measured the same way, but the distances vary depending on how far north or south of the equator.

To find out where you are with a GPS, you need a map that shows lines of latitude and longitude on it. The lines will be labeled on the map or along the borders of the map. Most nautical charts show the latitude measurements along the right the left border of the map. Longitude measuremnts will be shown along the top and bottom edges.
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