Answer
80.8 mi
Work Step by Step
Step 1. Use the figure given in the Exercise, angle $\angle C=180-42.3-68.9=68.8^{\circ}$
Step 2. Use the Law of Sines, we have $\frac{120}{sin68.8^{\circ}}=\frac{AC}{sin68.9^{\circ}}$ which gives $AC=120.08mi$
Step 3. The shortest distance (d) from the boat to the shore is the height of the triangle from C, thus $d=AC\cdot sin42.3^{\circ}\approx80.8mi$
