Question

Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristen’s home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 2 miles from her home. The football field is 8 miles from the library.

Answer 1

With that information you can determine how far the park is from the football field.

Call h the height of the triangle, x the distance from the park to the football field and y the distance from the park to the home of Kristen.

Using Pithagora's theorem, ou can state this system of equations:

1) From the complet triangle: x^2 + y^2 = (8 + 2)^2 = 10^2 = 100

2) From the triangle whose hypotenuse is the distance from the park to the football field:

x^2 = 8^2 + h^2

3) From the triangle whose hypotenuse is the distance from the park to the home of Kristen:

y^2 = 2^2 + h^2

To solve the system start by subtracting equation 3) from equation 1) =>

x^2 + y^2 = 100
y^2 = 4 + h^2
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x^2 = 100 - 4 - h^2

x^2 = 96 - h^2

Now sum this result to equation 2

x^2 = 96 - h^2
x^2 = 64 + h^2
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2x^2 = 96 + 64

2x^2 = 160

=> x^2 = 80

=> x = 8.94

Answer: 8.94 miles