Answer
Distance between home plate and second base is\[127.27\text{ feet}\].
Work Step by Step
The figure shows a square having a side of 90 foot.
All the angles of a square intersect each other at\[{{90}^{\circ }}\]. Therefore, the angle formed at first base, second base, third base and the home plate is\[{{90}^{\circ }}\].
Home plate, second base, and third base form a right triangle right angled at third base. Let the distance from third base to second base be \[a\]and the distance from home plate to third base be\[b\]. The distance from home plate to second base is given as \[x\].
Hence, \[a=90\]and\[b=90\].
Compute the value of \[c\]by using Pythagorean Theorem and substitute the value of a; and b into\[{{c}^{2}}={{a}^{2}}+{{b}^{2}}\]as shown below.
\[\begin{align}
& {{c}^{2}}={{a}^{2}}+{{b}^{2}} \\
& {{x}^{2}}={{90}^{2}}+{{90}^{2}}
\end{align}\]
Now, if\[{{90}^{2}}=90.90=8100\]then, complete the equation as follows:
\[\begin{align}
& {{x}^{2}}=8,100+8,100 \\
& {{x}^{2}}=16,200 \\
& x=\sqrt{16,200} \\
& =127.27
\end{align}\]
