Answer
a. $11110\ ft$
b. $ 4556\ ft$
c. $4162\ ft$
Work Step by Step
a. Step 1. Based on the given conditions, we can identify angle $\angle ABC=180^\circ-66^\circ=114^\circ$; thus angle $C=180^\circ-22^\circ-114^\circ=44^\circ$. We also know $1.6\ mi = 1.6\times5280=8448\ ft$
Step 2. Using the Law of Sines, we have $\frac{sin114^\circ}{b}=\frac{sin44^\circ}{8448}$; thus $b=\frac{8448sin114^\circ}{sin44^\circ}\approx 11110\ ft$
b. Using the Law of Sines, we have $\frac{sin22^\circ}{a}=\frac{sin44^\circ}{8448}$; thus $a=\frac{8448sin22^\circ}{sin44^\circ}\approx 4556\ ft$
c. Using the right triangle given in the figure of the exercise, we have $sin22^\circ=\frac{h}{b}$; thus $h=11110sin22^\circ\approx 4162\ ft$ or using another right triangle, $h=4556sin66^\circ\approx 4162\ ft$
