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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

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  • gnagner Apr 08, 2009

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



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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 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

Posted on Dec 19, 2008


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We can divide pilot's trip in 2 parts:
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