Answer
a. $493.8\ ft$
b. $343.0\ ft$
Work Step by Step
a. Step 1. Based on the given conditions, we can identify angle $\angle ABC=180^\circ-44^\circ=136^\circ$; thus angle $C=180^\circ-37^\circ-136^\circ=7^\circ$
Step 2. Using the Law of Sines, we have $\frac{sin37^\circ}{a}=\frac{sin7^\circ}{100}$; thus $a=\frac{100sin37^\circ}{sin7^\circ}\approx493.8\ ft$
b. Using the right triangle given in the figure of the exercise, we have $sin44^\circ=\frac{h}{a}$; thus $h=493.8sin44^\circ\approx343.0\ ft$
