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!!!
the included angle from boat to one lighthouse to the other call angle A.
No 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.
To determine how the angle between the sightings of two lighthouses can help the skipper decide when he is entering the danger zone, let's break down the problem and think step by step.
1. Recall that a semicircle is a half of a circle. In this case, the danger semicircle extends from one lighthouse to another.
2. Visualize the situation in your mind:
- Imagine the boat located somewhere on the water, represented by a point.
- Draw a line from the boat to each lighthouse, creating two lines or line segments. These are the "sightings" of the lighthouses from the boat's position.
- Now, imagine a semicircle extending between these two lines, with its center point lying on the line connecting the two lighthouses. One side of the semicircle connects to one lighthouse, and the other side connects to the second lighthouse.
3. Based on the description of the problem, the skipper knows that the water is too shallow inside the danger semicircle. Thus, he needs to ensure that he stays outside the danger semicircle to avoid grounding his boat.
4. Here's where the angle between the sightings comes into play:
- Consider the two lines forming the angle, which correspond to the sightings of the lighthouses. These lines should intersect at the boat's location.
- If the angle between the sightings is smaller than the angle subtended by the dangerous semicircle, it means the boat is located outside the dangerous area.
- If the angle between the sightings is equal to or larger than the angle subtended by the dangerous semicircle, it means the boat is located inside or on the edge of the dangerous semicircle.
5. Therefore, by measuring or estimating the angle between the sightings of the two lighthouses, the skipper can determine whether he is entering the danger zone.
It's worth noting that without any specific measurements or angles provided in the problem, we can only discuss the conceptually general idea. However, in practice, actual measurements may be necessary to accurately determine the angles and the danger zone.
I hope this explanation helps you understand how the angle between the sightings of the two lighthouses can assist the skipper in deciding when he is entering the danger zone.