# Geometry

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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 -

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

((5cos85,5sin50) + (6cos50,6sin50) and take their magnitude.

(the actual calculations are the same as above)

• Geometry -

THANK YOU

• Geometry -

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

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