A boat sails form port on a bearing of 290 degrees for 130 nm. How far north is it form its starting point?

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A boat sails form port on a bearing of 290 degrees for 130 nm. How far north is it form its starting point?
A 290 degree angle is equivalent to a -70 degree angle. Draw a -70 degree angle from the x axis, and call it theta. Let the length of the diagonal line be 130. Draw a line from the x axis to where the diagonal line ends; call the length of the second line y. sin(-70) = y/130. -.94 = y/130. y=-122.2 (rounded). This is 122.2 nm SOUTH from where it started.

Just use 130cos(290)

Or you can look at the diagram. 130sin(20). Same thing.

(b) as close as possible to B means that the line BD is perpendicular to the 050 bearing line and so AB is a hypotenuse

So use the basic cosine ratio:

cos 50 = BD/280

BD = 280 cos 50

BD = 179.98

So after walking for 180 m he is as close to B as he is going to get on the 050 bearing