Answer
14 inches ; $0.53$ inches
Work Step by Step
Here, $\tan \theta=\dfrac{h}{20+a}=\dfrac{6}{a}$
This implies that
$h=\dfrac{120}{a}+6$
or, $h=\dfrac{120}{15}+6=14$
Here, $h=\dfrac{120}{a}+6 \implies \dfrac{dh}{da}=\dfrac{-120}{a^2}$
Plug $da=1; a=15$
Thus, $dh=\dfrac{-120}{(15)^2}\approx 0.53$ inches
Hence, height is 14 inches and the error in measurement is $0.53$ inches
