```Question 585918
<pre>
{{{drawing(400,2000/9,-3,15,-1,9,
locate(0,0,BOAT), locate(11.7,4,80ft),locate(8.6,7.6,"35°"),
locate(11.425,0,BASE), red(arc(11.425,8,4,-4,180,215)),
blue(line(0,0,11.425,0)), line(11.425,0,11.425,8),red(line(11.425,8,0,0)),
green(line(7.5,8,15,8)), red(arc(0,0,4,-4,0,35)),locate(2,1,"35°"),
locate(6,0,x)

)}}}

The object BELOW is the boat and the object ABOVE is the top of the
cliff.

The angle of DEPRESSION is the horizontal from an object ABOVE looking
DOWNward to an object BELOW.

The angle of ELEVATION is the horizontal from an object BELOW looking
UPward to an object ABOVE.

They are always the same angle because they are alternate interior angles
formed when a tranversal (the line of sight) cuts two parallel (horizontal) lines.

So they are both 35°.

In the right triangle, the side opposite 35° is 80 and the side adjacent
35° is x which is what we are to find, so the trig ration that involves
what we are given *the opposite) and what we are to find *the adjacent

tan(35°) = {{{80/x}}}

Multiply both sides by x

x·tan(35°) = 80

Divide both sides by tan(35°)

x = {{{80/tan("35°")}}} = 114.24 feet

Edwin</pre>

```