Locations of Jack's home, school, and gym form an obtuse triangle on the map.

Let A be the difference between the distance from Jack's home to the school and the distance from the home to the gym. Let B be the distance from the school to the gym.

Is A greater than B, B greater than A, A equal to B, or can't be determined?

Why would it not be A greater than B? By the Triangle Inequality a + b > c for any triangle to exist. A picks any two sides which must be greater than the distance of a single side.

can't be determined. If the sides of a triangle are a,b,c from least to greatest, you must have

b-a < c < b+a
since you have not specified the obtuse angle in your diagram, there is no way to determine which side is the longest.

I get the feeling you want A < B, and that may be so, bu it cannot be determined from what you said.

From the given information, we know that the locations of Jack's home, school, and gym form an obtuse triangle on the map. However, we do not have the exact distances between these locations. Therefore, we cannot determine whether A is greater than B, B is greater than A, or if A is equal to B. The relationship between A and B will depend on the specific distances between the locations of Jack's home, school, and gym.

To determine whether A is greater than B, B is greater than A, or if A is equal to B, we need more information. We know that the locations of Jack's home, school, and gym form an obtuse triangle, but that information alone is not enough to compare the distances A and B.

To find the answer, we need the actual lengths of each side of the triangle formed by Jack's home, school, and gym. Once we have the lengths of these sides, we can calculate A and B.

To measure the lengths of the sides, you would need a scale map or GPS coordinates of the locations. By using a scale map, you can measure the distances between the locations accurately. Alternatively, with GPS coordinates, you can calculate the distances using the Haversine formula, which takes into account the curvature of the Earth.

Once you have the lengths of each side, you can subtract the distance from Jack's home to the gym from the distance from Jack's home to the school to calculate A. Then, you can compare A to B to determine which is greater, or if they are equal.

Without the specific measurements of the sides, it is not possible to determine whether A is greater than B, B is greater than A, or if A is equal to B.