Question

Suppose a park is located 1.2 miles east of your home. The library is 1.6 miles north of the park. What is the shortest distance between your home and the​ library?
Question content area bottom
Part 1
The shortest distance between your home and the library is
  
enter your response here miles.
​(Type an integer or a​ decimal.)

Answer 1

To find the shortest distance between your home and the library, you can use the Pythagorean theorem.

1. The distance from your home to the park is 1.2 miles east.
2. The distance from the park to the library is 1.6 miles north.

These two distances form a right triangle, where:
- The horizontal leg (eastward distance) is 1.2 miles.
- The vertical leg (northward distance) is 1.6 miles.

You can use the Pythagorean theorem, which states:

\[
c = \sqrt{a^2 + b^2}
\]

where \(c\) is the hypotenuse (the shortest distance from your home to the library), and \(a\) and \(b\) are the legs of the triangle.

In this case:

- \(a = 1.2\)
- \(b = 1.6\)

Now plug in these values:

\[
c = \sqrt{(1.2)^2 + (1.6)^2}
\]

Calculating the squares:

\[
c = \sqrt{1.44 + 2.56}
\]
\[
c = \sqrt{4.00}
\]
\[
c = 2.0
\]

Thus, the shortest distance between your home and the library is **2.0 miles**.