To find the distance from home base to second base on a baseball diamond, we can apply the Pythagorean theorem. The bases form a right triangle where the distance between first base and home plate is one leg of the triangle, the distance between second base and first base is the other leg, and the distance from home plate to second base is the hypotenuse.
Given that the distance between each base is 90 feet, we can set this up as follows:
Let \( a = 90 \) feet (from home to first base)
Let \( b = 90 \) feet (from first base to second base)
Let \( c \) be the distance from home to second base.
Using the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \] \[ c^2 = 90^2 + 90^2 \] \[ c^2 = 8100 + 8100 \] \[ c^2 = 16200 \]
Now, we take the square root of 16200:
\[ c = \sqrt{16200} \approx 127.3 \text{ ft} \]
So the correct response is:
90 squared plus 90 squared is equal to c squared ; 127.3 ft