Question

pythagorean theorem at the baseball field
fun facts:
on a baseball diamond
...
between home plate and
... is 90 feet
the pitchers mound is in the center of
...
draw what you know:
draw a sketch of a baseball field and label all the measurements (
& angles) you know from the given information.
solve it:
with the given information, can you use the pythagorean
distance between second base and home plate? show

Explanation:

Step1: Identify the triangle type

The baseball diamond is a square, so the distance from home to first base (\(a = 90\) ft) and first base to second base (\(b = 90\) ft) form a right - triangle with the distance from home to second base (\(c\)) as the hypotenuse.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\). Substitute \(a = 90\) and \(b = 90\) into the formula:
\(c^{2}=90^{2}+90^{2}=8100 + 8100=16200\)

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{16200}=\sqrt{8100\times2}=90\sqrt{2}\approx90\times1.414 = 127.26\) (ft)

Answer:

The distance between second base and home plate is \(90\sqrt{2}\) feet (or approximately \(127.26\) feet).