Answer
$h=14ft\pm0.53in$
Work Step by Step
Step 1. Identify the given quantities: pole height $b=6ft$, distance from lamp $d=20ft$, shadow length $a=15ft\pm1in$.
Step 2. Since $1~in=1/12ft$, we have $\frac{da}{a}=\frac{1/12}{15}=\frac{1}{180}$
Step 3. Using the figure given in the exercise and similar triangles, we have $\frac{b}{h}=\frac{a}{a+20}$ and $h=\frac{b(a+20)}{a}=b+\frac{20b}{a}=6+\frac{120}{a}=6+\frac{120}{15}=6+8=14ft$
Step 4. To estimate the error, differentiate $h$; we have $dh=-\frac{120da}{a^2}=-\frac{120/12}{15^2}=-\frac{2}{45}ft=-\frac{2(12)}{45}=-\frac{8}{15}in\approx0.53in$
Step 5. The lamppost height can be estimated to be $h=14ft\pm0.53in$
