SOLUTION: A rope is 10 feet longer than the height of a vertical pole. If the pole is attached to the top of the pole and stretched to the ground, the bottom end of the rope is 40 feet from

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A rope is 10 feet longer than the height of a vertical pole. If the pole is attached to the top of the pole and stretched to the ground, the bottom end of the rope is 40 feet from       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 596638: A rope is 10 feet longer than the height of a vertical pole. If the pole is attached to the top of the pole and stretched to the ground, the bottom end of the rope is 40 feet from the base of the pole. What is the height, in feet, of the pole?
Answer by KMST(5398) About Me  (Show Source):
You can put this solution on YOUR website!
Let the height of the pole be x feet.
The ground (horizontal), the pole (vertical), and the stretched rope form a tight triangle.
The rope is the hypotenuse, with length x%2B10 feet.
The lengths (in feet) of the legs of the triangle are x and 40.
Applying Pythagoras,
x%5E2%2B40%5E2=%28x%2B10%29%5E2 --> x%5E2%2B1600=x%5E2%2B20x%2B100
Subtracting x%5E2 from both sides of the equal sign,
1600=20x%2B100 --> 1600-100=20x%2B100-100 --> 20x=1500 --> 20x%2F20=1500%2F20 --> x=highlight%2875%29