Answer
$\approx$ 104 ft
Work Step by Step
Using the diagram in the book, annotate
with $h_{1}$, the part of the flagpole above the line of eyesight, and
with $h_{2}$, the part below the line of eyesight.
We know that $h_{1}+h_{2}=60.$
Upper triangle:
$\displaystyle \tan 18^{o}=\frac{h_{1}}{x} \ \Rightarrow \ h_{1}=x\tan 18^{o}$
Lower triangle: $h_{2}=x\tan 14^{o}$
Now,
$h_{1}+h_{2}=60.$
$x\tan 18^{o}+x\tan 14^{o}=60$
$x(\tan 18^{o}+\tan 14^{o})=60$
$ x=\displaystyle \frac{60}{\tan 18^{o}+\tan 14^{o}}\approx$104.48452836$\approx$ 104 ft
