Answer
$9.2\ mi$ (from B) and $5.7\ mi$ (from A)
Work Step by Step
Step 1. Based on the given conditions, draw a diagram as shown in the figure.
Step 2. We can identify angle $A=90^\circ-25^\circ=65^\circ$, angle $B=90^\circ-56^\circ=34^\circ$, and angle $F=180^\circ-65^\circ-34^\circ=81^\circ$
Step 3. Using the Law of Sines, we have
$\frac{sin65^\circ}{a}=\frac{sin81^\circ}{10}$, thus $a=\frac{10sin65^\circ}{sin81^\circ}\approx9.2\ mi$
Step 4. Similarly, we have $\frac{sin34^\circ}{b}=\frac{sin81^\circ}{10}$; thus $b=\frac{10sin34^\circ}{sin81^\circ}\approx5.7\ mi$
