Posted by **Saman** on Friday, August 23, 2013 at 8:19am.

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**, Friday, August 23, 2013 at 8:53am
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**, Friday, August 23, 2013 at 9:02am
THANK YOU

- Geometry -
**Steve**, Friday, August 23, 2013 at 12:43pm
Are we worried whether we use compass headings where North = 0 degrees, rather than East, and angles are measured clockwise?

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