Question

The rocks near the shore between two lighthouses at points A and B make the waters unsafe. The measure of arc AXB is 300. Waters inside this arc are unsafe. Suppose you are a navigator on a ship at sea. How can you use the lighthouses to keep the ship in safe waters?

Answer 1

A navigator can keep a ship in safe waters by maintaining a course where the two lighthouses at points A and B remain aligned outside of the dangerous 300-degree arc. The alignment acts as a guide to stay clear of the rocks between the lighthouses.

Step-by-step explanation:

To keep the ship in safe waters while navigating between two lighthouses at points A and B, a navigator should maintain a course that keeps the lights from A and B aligned in a manner that the ship does not cross the unsafe 300-degree arc AXB. If the lights of A and B are in line with each other when viewed from the ship, the navigator is directly on the line connecting A and B. The navigator should keep this alignment to a bearing which ensures that the ship stays outside of the dangerous arc.

By continuously adjusting the ship's bearing to keep the lighthouses aligned and out of the 300-degree dangerous arc, the navigator will ensure the ship remains in safe waters. It's important to note that this method relies on having a clear view of both lighthouses and good visibility conditions.

Answer 2

In order to keep the ship in safe waters, we can first make use of the distance between the lighthouses, as well as the 60-degree central angle in order to find the radius and center of the circle. In this way, we can set a considerable distance.