Katrina lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Katrina’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 4 miles from her home. The football field is 18 miles from the library.

Question

Katrina lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Katrina’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 4 miles from her home. The football field is 18 miles from the library.
a. How far is the library from the Park?
b. How far is the park from the football field?

Steve · Answer

using similar triangles, you can see that PH/4 = 18/PH PH^2 = 72 PH^2 + PF^2 = 18^2 PL/4 = PF/PH