Question

At a distance of 34 feet from the base of a flag pole, the angle of elevation to the top of a flag is 48.6°. The flag itself is 5.1 feet tall. The angle of elevation to the bottom of the flag is 44.6°. The pole extends 1 foot above the flag.

Find the height of the pole.

Answer 1

for h2, the height from the base to the top of the flag:
h2/34 = tan 48.6°
h2 = 34tan48.6°
= ..

for h1, the height to the bottom of the flag
h1/34 = tan 44.6°
h1 = 34tan44.6°

h2-h1 = 5.1
(this information is not needed
when I calculate h2 - h1, I get 5.04 , not 5.1.
It looks like they rounded off intermediate answers, which is a no-no)

Actually , all we needed to find the height of the pole is
34tan48.6° + 1