To find the distance from home plate to second base in a baseball diamond, you can use the Pythagorean theorem. The distance between bases is 90 feet, forming a right triangle where each leg is the length of the base, and the distance you're looking for is the hypotenuse.
Using the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
In this case, both \(a\) and \(b\) are 90 feet (the distance between home plate to first base and first base to second base):
\[ c^2 = 90^2 + 90^2 \] \[ c^2 = 8100 + 8100 \] \[ c^2 = 16200 \] \[ c = \sqrt{16200} \] \[ c \approx 127.3 \text{ feet} \]
So the correct distance from home base to second base is approximately 127.3 feet.
Thus, the option that reflects this calculation is: 902 + 902 = c² ; 127.3 ft.