Respuesta :
In a triangle formed by Anna, Ben, and Cathy during their treasure hunt, the two friends who are farthest apart are the ones whose positions create the longest side of the triangle. To determine this, you need to consider the concept of triangle inequality.
1. **Triangle Inequality Theorem**: According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
2. **Identify the Longest Side**: Compare the distances between each pair of friends to find the longest side of the triangle. The two friends associated with this longest side are the ones farthest apart.
3. **Measure Distances**: Calculate the distances between Anna and Ben, Ben and Cathy, and Cathy and Anna to determine which pair is farthest apart based on the longest side of the triangle.
4. **Conclusion**: The two friends whose distances form the longest side of the triangle are the ones who are farthest apart during the treasure hunt.
By applying the triangle inequality theorem and analyzing the distances between Anna, Ben, and Cathy, you can identify which two friends are farthest apart based on the geometry of the triangle they form.
