The skipper of a boat knows that the water is too shallow to bring his boat inside a "danger semicircle" that goes from lighthouse to lighthouse. How can the angle between his sightings of the two lighthouses help him decide when he is entering the danger zone?

How can I figure this out. There is a picture, but there aren't any numbers or angles on it. It seems to be a theory problem and I reread my book's section on this and still do not get it.

Please help me!!!

geometry - bobpursley, Saturday, December 5, 2009 at 7:49pm
the included angle from boat to one lighthouse to the other call angle A.

Now if the boat is on the perimeter of the semicircle, that angle A is 90 deg.
If outside the circle, the angle will be less.

this answer I still do not understand. How can the angle between his sightings help him decide when he is entering the danger zone?

Can anyone explain this further? I appreciate it.

http://mathblog1234.files.wordpress.com/2009/08/angles-in-a-semi-circle-equals-to-90-degrees.jpg

APB is 90 degrees anywhere on the circle. Outside, it is a smaller angle.

To understand how the angle between his sightings of the two lighthouses can help the skipper decide when he is entering the danger zone, let's break it down step by step:

1. Imagine the skipper's boat is at a particular point in the water, and he can see two lighthouses from his position.

2. The line formed by connecting the skipper's boat to each lighthouse creates an angle, let's call it angle A. This angle represents the direction the skipper is looking towards the lighthouses.

3. Now, let's consider the scenario where the skipper is at the edge of the danger zone or just entering it. In this case, the line connecting the skipper's boat to the two lighthouses will form a right angle, or 90 degrees. This means angle A would measure 90 degrees.

4. However, if the skipper is outside the danger zone, the line connecting his boat to the lighthouses will form an acute angle, smaller than 90 degrees. As he moves further away from the danger zone, the angle will become smaller.

Based on this understanding, the skipper can use the angle between his sightings of the two lighthouses to determine whether he is entering the danger zone or not. If the angle is close to 90 degrees, he is likely at the edge of the danger zone, signaling him to be cautious. But if the angle is smaller, he knows he is still far from the danger zone and can navigate safely.

Please note that this explanation is based on the assumption that the danger zone is a semicircle between the two lighthouses, and that the angle formed by connecting the skipper's boat to the lighthouses can be measured or estimated accurately. Additionally, this explanation assumes that the skipper knows the exact location of the lighthouses and the boundaries of the danger zone.