A baseball diamond is a square with sides 22.4m. The pitchers mound is 16.8m from home plate on the line joining home plate and second base. How far is the pitchers mound from first base? Step by step please.

To find the distance from the pitcher's mound to the first base, we can use the Pythagorean theorem. Here are the steps:

Step 1: Draw a diagram representing the baseball diamond, with the pitcher's mound, home plate, and first base.

Step 2: Identify the relevant sides of the right triangle. The distance from home plate to first base is one side (let's call it a), the distance from home plate to the pitcher's mound is the hypotenuse (let's call it c), and the distance from the pitcher's mound to first base is the other side (let's call it b).

Step 3: Use the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In equation form, it is written as: c^2 = a^2 + b^2.

Step 4: Substitute the given values into the equation. We know that the side a (distance from home plate to first base) is the length of one side of the baseball diamond, which is 22.4m. We also know that the side c (distance from home plate to the pitcher's mound) is given as 16.8m.

Step 5: Solve the equation for side b (distance from the pitcher's mound to first base). Rearranging the Pythagorean theorem equation, we have b^2 = c^2 - a^2.

Plugging in the values, we have b^2 = (16.8m)^2 - (22.4m)^2.

Step 6: Calculate the value of b using a calculator. Take the square root of the right side of the equation to solve for b. Once you do that, you will get the distance from the pitcher's mound to first base.

By following these steps, you can determine the exact distance from the pitcher's mound to first base.