Question

The bearing of a ship from a lighthouse was found to be n14 degrees14°e. after the ship sailed 7.27.2 miles dueâ south, the new bearing was n31 degrees31°e. find the distance between the ship and the lighthouse at each location.

Answer 1

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

BL = 5.96 miles