Answer
The required solution is $\text{1815}\ \text{miles}$
Work Step by Step
The angle $\theta $ between Miami and the equator is $26{}^\circ $.
Now, convert it into radians:
$\begin{align}
& \theta =26{}^\circ \\
& =26{}^\circ \left( \frac{\pi }{180{}^\circ } \right) \\
& =\frac{13\pi }{90}
\end{align}$
And the radius $r$ of the earth is $4000\ \text{miles}$.
The distance $s$ between Miami and the equator is given by
$s=r\theta $
Put $4000\ \text{miles}$ for $r$ and $\frac{13\pi }{90}$ for $\theta $:
$\begin{align}
& s=4000\ \text{miles}\left( \frac{13\pi }{90} \right) \\
& =\frac{5200\pi \ \text{miles}}{9}
\end{align}$
Put $\pi =3.14159$:
$\begin{align}
& s=\frac{5200\left( 3.14159 \right)\ \text{miles}}{9} \\
& =1815.14\ \text{miles}\approx \text{1815}\ \text{miles}
\end{align}$
Hence, Miami, Florida is $\text{1815}\ \text{miles}$ north of the equator.
