Question 1195054
<pre>

{{{drawing(400,240,-2,8,-1,5,

locate(-1.1,2,x), locate(5,.5,theta),

line(0,0,-.8316467633,3.912590403),
locate(2.8,2.5,35),
locate(-.3,2.1,20),
line(-3,0,9,0),locate(-.8,1.3,12^o),red(arc(-.8316467633,3.912590403,6.5,-6.5,270,282)),
red(arc(7,0,6.5,-6.5,154,180)), 

line(7,0,-.8316467633,3.912590403),green(line(-.8316467633,3.912590403,-.8316467633,0)) )}}}

First we find x, the distance from the top of the tree to the ground:

Using the smaller right triangle on the left:

{{{x/20}}}{{{""=""}}}{{{adjacent/hypotenuse}}}{{{""=""}}}{{{cos(12^o)}}} 

{{{x/20}}}{{{""=""}}}{{{cos(12^o)/1}}}

Cross-multiply

{{{x}}}{{{""=""}}}{{{20cos(12^o)}}}

Then, using the large right triangle: 

{{{x/35}}}{{{""=""}}}{{{opposite/hypotenuse}}}{{{""=""}}}{{{sin(theta)}}}

{{{(20cos(12^o))/35}}}{{{""=""}}}{{{sin(theta)}}}

{{{0.5589414861}}}{{{""=""}}}{{{sin(theta)}}}

{{{theta}}}{{{""=""}}}{{{33.98262602^o}}}

Rounding to the nearest degree, about 34<sup>o</sup>

Edwin</pre>