SOLUTION: PROBLEM: HEIGHT OF A DOCK: A BOAT IS BEING PULLED INTO A DOCK WITH A ROPE ATTACHED TO THE BOAT AT WATER LEVEL. WHEN THE BOAT IS 12ft FROM THE DOCK, THE LENGTH OF THE ROPE FROM THE

Algebra ->  Triangles -> SOLUTION: PROBLEM: HEIGHT OF A DOCK: A BOAT IS BEING PULLED INTO A DOCK WITH A ROPE ATTACHED TO THE BOAT AT WATER LEVEL. WHEN THE BOAT IS 12ft FROM THE DOCK, THE LENGTH OF THE ROPE FROM THE      Log On


   

Question 143953This question is from textbook College Algebra
: PROBLEM: HEIGHT OF A DOCK:
A BOAT IS BEING PULLED INTO A DOCK WITH A ROPE ATTACHED TO THE BOAT AT WATER LEVEL. WHEN THE BOAT IS 12ft FROM THE DOCK, THE LENGTH OF THE ROPE FROM THE BOAT TO THE DOCK IS 3ft LONGER THAN TWICE THE HEIGHT OF THE DOCK ABOVE THE WATER. FIND THE HEIGHT OF THE DOCK.
*** ON THIS PROBLEM I AM BASICALLY MISSING THE WHOLE CONCEPT OF HOW TO CORRECTLY SET AND FIND THE MATERIAL TO WORK IT OUT... ALTHOUGH I WOULD PERFER SOMEONE TO PLEASE WORK IT OUT STEP BY STEP SO I COULD VISUALLY SEE WHAT ALL I AM DOING WRONG.. THANKS :) This question is from textbook College Algebra

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
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+%2B+2h
The remaining side of the triangle is the height of the dock

|
|
|h
|-------------
12
Now you can use the Pythagorean theorem.
c%5E2+=+a%5E2+%2B+b%5E2
%283%2B2h%29%5E2+=+12%5E2+%2B+h%5E2+
9+%2B+12h+%2B+4h%5E2+=+144+%2B+h%5E2
3h%5E2+%2B+12h+-+135+=+0+
h%5E2+%2B+4h+-+45+=+0+
%28h%2B9%29%28h-5%29+=+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%5E2+%2B+12%5E2+=+13%5E2