Question

A boat is being pulled into a dock with a rope attached to the boat at water level. When the boat is 12 feet from the dock, the length of the rope form the boat to the dock is 3 feet longer than twice the height of the dock above the water. Find the height of the dock.

Answer 1

Given :

A boat is being pulled into a dock with a rope attached to the boat at water level. When the boat is 12 feet from the dock, the length of the rope form the boat to the dock is 3 feet longer than twice the height of the dock above the water.

To Find :

The height of the dock.

Solution :

This will make a right angle triangle as given in link below .

Now , applying Pythagoras theorem :

$(2h+3)^2=h^2+12^2\\\\4h^2+9h+9=h^2+144\\\\h^2+4h-45=0\\\\(h-5)(h+9)=0$

Now , h = 5 or h = -9 .

Now , height cannot be negative .

So , height of the dock is 5 ft .

Hence , this is the required solution .