Question 143953
In your mind, imagine a triangle.

One side of the triangle is the distance from the boat to the dock (given as 12)
The hypotenuse of the triangle is the rope. It is given as {{{3 + 2h}}}
The remaining side of the triangle is the height of the dock


|
|     
|h       
|-------------
      12

Now you can use the Pythagorean theorem.

{{{c^2 = a^2 + b^2}}}
{{{(3+2h)^2 = 12^2 + h^2 }}}
{{{9 + 12h + 4h^2 = 144 + h^2}}}
{{{3h^2 + 12h - 135 = 0 }}}
{{{h^2 + 4h - 45 = 0 }}}
{{{(h+9)(h-5) = 0 }}}

h = -9 or h = 5

Since the height of the cannot be below the water line, the height must be 5.

Check your answer. Is {{{5^2 + 12^2 = 13^2}}}