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2 answers:
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Imagine right triangle PHF, where P - park, H - home and F - football field, then PH, PF are legs and HF is hypotenuse . Denote point L to be library. You know that point L lies on the segment FH and FL=8, LH=2. Also you know that PL is an altitude to the hypotenuse.
Use the property of altitude drawn from the vertex of right angle to the hypotenuse (the length of the altitude is geometrical mean between legs' projections onto hypotenuse):
mi.
This means that the distance between park and libriry is 4 miles.
Consider right triangle PLF ( angle L is right angle and PF - hypotenuse). By the Pythagorean theorem,
mi. The distance between park and football field is
miles.
Answer: the distance between park and libriry is 4 miles and the distance between park and football field is miles.
The answer is: 
The explanation is shown below:
1. You have the following expression given in the exercise above:
2. By applying the distributive property, you obtain:
3. Now, you must factor
in the numerator and 
in the denominator:
4. Simplify:
The explanation is shown below:
1. You have the following expression given in the exercise above:
2. By applying the distributive property, you obtain:
3. Now, you must factor
4. Simplify:
Answer:
7
Step-by-step explanation:
Using Pythagoras' identity on the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
let x be the other leg, then
x² + 4² = ( )²
x² + 16 = 65 ( subtract 16 from both sides )
x² = 49 ( take the square root of both sides )
x = = 7
That is the other leg is 7 units