$1.)$ In an attempt to determine the height of one of the Liberty statues atop the Liberty Building in downtown Buffalo, I walked directly backwards from the bottom of the building until my eyes made a line$-$of$-$sight at an angle of inclination of $45$ to the bottom of the statue. I continued to walk directly backwards precisely $100$ more feet and now found the angle of inclination of my eyes to the bottom of the statue to be $37\mathrm{.}56.$ From that location, I then looked directly at the top of the statue and found the angle of inclination to be $40\mathrm{.}437.$

How tall is the statue?