Question

24 given the figure below, what is the distance from home base to 2nd base? round to the nearest thousandth. 127.279 feet 2nd base 3rd base 1st base 90 ft. home plate

Explanation:

Step1: Identify right triangle sides

The distance from home to 2nd base forms the hypotenuse of a right triangle with legs each 90 ft.

Step2: Apply Pythagorean theorem

Use $c = \sqrt{a^2 + b^2}$, where $a=90$, $b=90$.
$$c = \sqrt{90^2 + 90^2}$$

Step3: Simplify the expression

Calculate the sum of squares and simplify the root.
$$c = \sqrt{8100 + 8100} = \sqrt{16200} = 90\sqrt{2}$$

Step4: Compute decimal value

Calculate the numerical value and round to thousandths.
$$90\sqrt{2} \approx 90 \times 1.41421356 \approx 127.2792204$$

Answer:

127.279 feet