tough question

Question

AN AIRPLANE TRAVELS AT 160 KM/HR FOR 2 HOURS IN A DIRECTION OF 200° AT THE END OF THIS TIME, HOW FAR SOUTH OF THE AIRPORT IS THE AIRPLANE? NOTE DIRECTIONS ARE GIVEN IN DEGREES CLOCKWISE FROM NORTH.

 

THE AIRPLANE IS ----KILOMETERS SOUTH OF THE AIRPORT AFTER 2 HOURS.

Answer 1

Assuming North to be at 90º, rotating from 90º clockwise 200º (-200º) puts the plane in a direction of 90º-200º = -110º, equivalent to flying in a direction of 250º (in a standard coord. system) and distance of 320km.  The distance south will be:  

 

Either of the following 2 facts is useful in drawing a triangle to visualize the problem:

     250º is 70º past 180º                    250º is 20º from 270º

 

   sin70º = x/320             OR             cos20º= x/320   <==depending on how you drew your triangle.  Either way,

 

          x = 320 * sin70º                       x = 320cos20º

 

                           x = 300.7km south of the airport

 

THE AIRPLANE IS 300.7 KILOMETERS SOUTH OF THE AIRPORT AFTER 2 HOURS.