Question

In Princeton, the library is due south of the courthouse and due west of the community swimming pool. If the distance between the library and the courthouse is 7 miles and the distance between the courthouse and the city pool is 8 miles, how far is the library from the community pool? If necessary, round to the nearest tenth.

Please respond.

Thank you!

Answer 1

3.87 miles

Explanation:

The attached figure gives the relative locations of the courthouse, the library and the pool.

The three locations represent a right triangle with the distance between courthouse - pool as the hypotenuse and the distance between courthouse - library as the vertical leg

By the Pythagorean theorem if c is the hypotenuse and a, b the other two legs

`c^2 = a^2 + b^2`

a = distance between courthouse and library = 7 miles
c = distance between courthouse and pool = 8 miles
and we have to find b

So plugging in known values

`8^2 = 7^2 + b^2\\\\b^2 = 8^2 - 7^2\\\\b^2 = 64 - 49\\\\b^2 = 15\\\\b= √(15) = 3.87298 \approx 3.87 \;miles`