The bearing of a ship from a lighthouse was found to be n14 degrees14â°e. after the ship sailed 7.27.2 miles dueâ south, the new bearing was n31 degrees31â°e. find the distance between the ship and the lighthouse at each location.

To solve this problem, let us first assign some reference points. Let us say that initial position of the ship is called point A while the final position is called point B. While the position of the light house is called point L. Together they form a triangle.

The angles are:

angle LAB = 14°

angle ABL = (180 – 31)° = 149°

The lighthouse is at L.
The ship sails 7.2 miles to B.

We see that angle angle ALB = 180 – angle LAB – angle ABL

Therefore

angle ALB = 180 – 14 – 149 = 17°

 
Now in the triangle ABL, we use the Law of Sines:

AL / sin 149 = 7.2 / sin 17

AL = 12.68 miles

BL / sin 14 = 7.2 / sin 17

seeing the graph would