Question

a baseball diamond is really a 90 foot square. lets say the catcher is throwing the ball from home to second base: use pythagorean theorem to find out how far he throws the ball. 90 feet 90 feet 3rd 1st 90 feet 90 feet home a² + b² = c²

Explanation:

Step1: Identify the sides of the right - triangle

In a square (baseball diamond), when considering the throw from home to second base, the two sides of the right - triangle (the sides of the square) are \(a = 90\) feet and \(b = 90\) feet. The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the length of the hypotenuse (the distance from home to second base).

Step2: Substitute the values into the Pythagorean theorem

Substitute \(a = 90\) and \(b = 90\) into \(a^{2}+b^{2}=c^{2}\). We get \(90^{2}+90^{2}=c^{2}\).

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Step3: Solve for \(c\)

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

Answer:

The catcher throws the ball approximately \(127.26\) feet.