A ship is sailing east. At one point the bearing of a submerged rock is at 45 degrees 20 minutes. The ship sails for 15.1 miles and then the rock is at at a bearing of 306 degrees 41 minutes. What the distance of the rock at the later point?

I strongly advise you to make a sketch for this. You will get a triangle formed by the direction the ship is sailing, the first line indicating where the rock is and a second line on which the rock is found. Where the two latter lines meet is the position of the rock. Using the angles and the distance the ship sailed and using the sine rule, you can easily get the answer to your question :)

Could you try this and post what you get?