Is the Bermuda Triangle really a triangle? The Bermuda Triangle features vertices in Miami, Florida; Bermuda; and San Juan, Puerto Rico. Find the distances between these points and remember to keep all measures in the same units. Using what you have learned about triangles, determine if the Bermuda Triangle is really a triangle. Units used:

Question

Fill out the table with the distance between each point on the Bermuda Triangle:
Points- Miami, FL to Bermuda. Distance -?
Points - Bermuda to San Juan, Puerto Rico - Distance -?
San Juan, Puerto Rico to Miami, FL. Distance- ?
Apply the Triangle Inequality Theorem
Is the Bermuda Triangle really a triangle? Explain

Answer 1

To determine if the Bermuda Triangle forms a triangle, we can apply the Triangle Inequality Theorem, which states that for any triangle with sides of lengths \( a \), \( b \), and \( c \):

1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)

First, let's calculate the distances between the vertices of the Bermuda Triangle:

1. Miami, FL to Bermuda: The distance from Miami International Airport (MIA) to L.F. Wade International Airport (BDA) in Bermuda is approximately 1,030 miles (1,658 kilometers).

2. Bermuda to San Juan, Puerto Rico: The distance from Bermuda to Luis Muñoz Marín International Airport (SJU) in San Juan is approximately 1,247 miles (2,009 kilometers).

3. San Juan, Puerto Rico to Miami, FL: The distance from San Juan to Miami is approximately 1,059 miles (1,703 kilometers).

Now, we can summarize this information in a table:

| Points | Distance (Miles) | |--------------------------------------|-------------------| | Miami, FL to Bermuda | 1,030 | | Bermuda to San Juan, Puerto Rico | 1,247 | | San Juan, Puerto Rico to Miami, FL | 1,059 |

Next, we will apply the Triangle Inequality Theorem using the established distances.

Let:

• \( a = \) Distance Miami to Bermuda = 1,030 miles
• \( b = \) Distance Bermuda to San Juan = 1,247 miles
• \( c = \) Distance San Juan to Miami = 1,059 miles

Checking the triangle inequalities:

1. \( a + b > c \)

   • \( 1,030 + 1,247 > 1,059 \)
   • \( 2,277 > 1,059 \) ✔️ (True)

2. \( a + c > b \)

   • \( 1,030 + 1,059 > 1,247 \)
   • \( 2,089 > 1,247 \) ✔️ (True)

3. \( b + c > a \)

   • \( 1,247 + 1,059 > 1,030 \)
   • \( 2,306 > 1,030 \) ✔️ (True)

Conclusion:

Since all three conditions of the Triangle Inequality Theorem are satisfied, we conclude that the distances between Miami, Bermuda, and San Juan allow for the formation of a triangle. Therefore, yes, the Bermuda Triangle is indeed a triangle based on the distances between these points.