Question 938291
Who walks around with a protractor?
Let's call his original distance from the tree, {{{X}}}.
Then the second distance is {{{X-50}}}
The tree height is {{{H}}}.
{{{tan(34)=H/X}}}
{{{tan(54)=H/(X-50)}}}
So then,
{{{(H/X)/(H/(X-50))=tan(34)/tan(54)}}}
{{{(X-50)/X=0.49}}}
{{{X-50=0.49X}}}
{{{0.51X=50}}}
{{{X=98}}}{{{ft}}}
Then,
{{{H/98=0.6745}}}
{{{H=66.1}}}{{{ft}}}