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Question

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 3 ft longer than twice the heig of the dock above the water. Find the height of the dock.

Answer 1

Draw a diagram of a right triangle.

 

Let h = height of dock (vertical side of right Δ)

     12 ft = length of horizontal side of right Δ

    2h + 3 = length of hypotenuse

 

By the Pythagorean Theorem,  h² + 12² = (2h + 3)²

 

h² + 144 = 4h² + 12h + 9

 

            0 = 3h² + 12h - 135

 

            0 = (3h + 27) (h - 5)

 

h = -9 or h = 5.  Since the height of the dock can't be negative, h = 5 ft.