Sorry for asking another question, but I don't know how to set this problem up.

Ship A is due west of a lighthouse. Ship B is 12 km south of ship A. From ship B the bearing to the lighthouse is N63E. How far is ship A from the lighthouse?

tan 63º = x/12

solve for x

No problem at all! Let's break down the problem and set it up step by step.

1. Start by visualizing the situation. Ship A is due west of a lighthouse, so we can draw a line going straight west to represent the position of ship A. Ship B is 12 km south of ship A, so we can draw a straight line going south from ship A to represent ship B's location. Lastly, we know that from ship B, the bearing to the lighthouse is N63E.

2. To find the distance between ship A and the lighthouse, we need to use trigonometry. We can use the concept of right triangles and the tangent function to find the missing side.

3. Since the bearing N63E refers to a direction, we need to convert it to an angle. The bearing is measured clockwise from north, so N63E means we need to go 63 degrees from the north direction towards the east.

4. Now that we have the angle, we can draw a line from ship B towards the lighthouse. Since we know the angle and the side opposite to the angle (12 km, the distance between ship A and B), we can find the adjacent side, which represents the distance between ship B and the lighthouse.

5. Finally, we can use the trigonometric ratio tangent (tan) to find the distance between ship B and the lighthouse. The formula is: opposite side / adjacent side. In this case, the opposite side is 12 km, and the angle is 63 degrees.

By plugging in the values and applying the formula, you can calculate the distance between ship B and the lighthouse.