SOLUTION: If the bottom of a 17 foot ladder is 8 feet from the base of a chimney, how far is it from the bottom of the chimney to the top of the ladder?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: If the bottom of a 17 foot ladder is 8 feet from the base of a chimney, how far is it from the bottom of the chimney to the top of the ladder?       Log On


   

Question 715515: If the bottom of a 17 foot ladder is 8 feet from the base of a chimney, how far is it from the bottom of the chimney to the top of the ladder?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
It might help you understand if you draw a diagram. Make the chimney a vertical line segment. The ground will be a horizontal line. The ladder will be a slanted line segment from the chimney to the ground. The diagram should be a right triangle.

The base of the chimney is where the chimney (vertical) meets the ground (horizontal). From here to where the ladder touches the ground is 8 feet. The ladder (which is the hypotenuse for this triangle) is 17 feet.

We can use the Pythagorean Theorem to find the distance from the bottom/base of the chimney to where the ladder touches the chimney:
x%5E2%2B8%5E2=17%5E2
No we solve. Squaring the 8 and the 17:
x%5E2%2B64=289
Subtracting 64:
x%5E2=225
Square root (ignoring the negative square root because we do not want a negative height):
x+=+15
So the distance from the bottom/base of the chimney to where the ladder touches the chimney is 15 feet.