A sailboat....

Question

A sailboat leaves port on a bearing of S72°W. After sailing for two hours at 12 knots, the boat turns 90° toward the south. After sailing for three hours at 9 knots on this course, what is the bearing to the ship from the port?

Answer 1

From the port, the boat  sails 24 knots,  turning 90 degrees, sailing 27 knots.  That makes up a right triangle, with the longest side x, hence

24² + 27²  = x² ,   x = 36.12

 

Now, the length of the 24 knots from the port to the south is,

  24cos(72°) =  7.42

 

And the length of the 27 knots from the port to the south is,

  27cos(18°) = 25.68

 

The total length from the port to the south is,

  7.42 + 25.68 = 33.10

 

Therefore, the angle between the x and the total length

  cos^-1(33.10/36.12) = 23.6°

 

The answer is S23.6W