Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristens home and the football field at the exact points where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 4 miles from her home. The football field is 10 miles from the library.
How far is the library from the park?
How far is the park from the football field?
2√10 miles; 2√35 miles
To find the distance between the library and the park, we need to understand the geometry of the situation. Given that Kristen's home, the park, and the library form a right triangle, we can use the Pythagorean theorem to determine the distance.
Let's assume that Kristen's home is point A, the park is point B, and the library is point C. The distance from Kristen's home to the park can be represented as AB, the distance from the library to the park can be represented as BC, and the distance from Kristen's home to the library can be represented as AC.
Based on the given information, we know that AC (the distance from Kristen's home to the library) is 4 miles, and BC (the distance from the library to the park) is what we need to find.
Using the Pythagorean theorem, we can write the equation:
AB^2 + BC^2 = AC^2
Substituting the known values:
AB^2 + BC^2 = 4^2
AB^2 + BC^2 = 16
Now, let's calculate the distance BC:
BC^2 = 16 - AB^2
BC^2 = 16 - 10^2 (since we know the distance from the football field to the library is 10 miles)
BC^2 = 16 - 100
BC^2 = -84
Since we are dealing with distances, we cannot have a negative value. Therefore, there must be an error in the given information or the way we set up the problem. Please double-check the problem statement and provide additional information if available.