louisville is 14 mi due north of farmville, stanton is due east of farmville, and louisville is 25 mi from stanton.
how far apart are farmville & stanton? round to the nearest tenth (of a mile).
-- im not sure how to do this problem
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As you can see, that forms a right angle triangle.
a*2 + b^2 = c^2
14^2 + b^2 = 25^2
196 + b^2 = 625
b^2 = 429
b = 21 miles
20.7
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's represent the distances as follows:
- Distance from Farmville to Louisville: 14 miles (north direction)
- Distance from Farmville to Stanton: Let's label it as 'x' miles (east direction)
- Distance from Louisville to Stanton: 25 miles
We have a right triangle with sides of length 14 miles (north direction), x miles (east direction), and 25 miles. The distance between Farmville and Stanton can be found by finding the length of the remaining side of this right triangle.
Using the Pythagorean theorem, we can set up the following equation:
14^2 + x^2 = 25^2
Simplifying, we get:
196 + x^2 = 625
Now, let's solve for 'x':
x^2 = 625 - 196
x^2 = 429
x = √429 ≈ 20.72 (rounded to two decimal places)
Therefore, the distance between Farmville and Stanton, rounded to the nearest tenth, is approximately 20.7 miles.