Answer:
(a) 4 miles
(b) 8.9 miles
Step-by-step explanation:
(a) Theorem 1: In a right triangle, the altitude drawn from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of these two segments.
Hence, the distance d between the park and the library is
[tex]d^2=2\cdot 8\\ \\d^2=16\\ \\d=4\ miles[/tex]
(b) Theorem 2: In a right triangle, the altitude drawn from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.
Thus, the distance D between the park and the football field is
[tex]D^2=8\cdot (2+8)\\ \\D^2=8\cdot 10\\ \\D^2=80\\ \\D=\sqrt{80}=4\sqrt{5}\approx 8.9\ miles[/tex]
