Posted by Saman on .
A ship sails 5 km from a port A on a bearing of 85 degrees and then 6 km on a bearing of 50 degrees. Calculate the distance and bearing from A.

Geometry 
Reiny,
calculate the horizontal and vertical replacements of each trip
first trip:
x/5 = cos85 , x = 5cos85
y/5 = sin85 , y = 5sin85
2nd trip:
x/6 = cos50 , x = 6cos50
y/6 = sin50 , y = 6sin50
total horizontal displacement
= 5cos85 + 6cos50 = appr 4.2925
total vertical displacement
= 5sin85 + 6sin50 = appr 9.5772
now use Pythagoras ... to get
√(4.2925^2 + 9.5772) = 40.4952
or
just add the vectors
((5cos85,5sin50) + (6cos50,6sin50) and take their magnitude.
(the actual calculations are the same as above) 
Geometry 
Saman,
THANK YOU

Geometry 
Steve,
Are we worried whether we use compass headings where North = 0 degrees, rather than East, and angles are measured clockwise?