Question 1036186
Let x = the distance of the foot of the axis of the arch from the vertex of angle {{{80^o}}}.

Then {{{tan80^o = h/x}}}, and {{{tan69^o = h/(x+131)}}}.

The first equation gives {{{x = h/tan80^o}}}.

Substituting this into the 2nd equation gives

{{{tan69^o = h/(h/tan80^o +131)}}}.

==> {{{tan69^o = (htan80^o)/(h+131tan80^o)}}}

==> {{{htan69^o + 131*tan80^o*tan69^o = htan80^o}}}

==> {{{h = (131*tan80^o*tan69^o)/(tan80^o - tan69^o) = 631.2}}} feet, the height of the Gateway Arch.