SOLUTION: I need help solving this with the pythagorean theorem. a ladder is leaning against a building so that the distance from the ground to the top of the ladder is 9 feet less than th

Click here to see ALL problems on Equations

Question 1010990: I need help solving this with the pythagorean theorem.
a ladder is leaning against a building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 15 feet
Found 4 solutions by fractalier, It is costly, addingup, MathLover1:
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website!
Make yourself a right triangle.
Call the hypotenuse, x, which is the length of the ladder.
The leg going up is x-9.
The base is 15 feet.
Use the Pythagrean Theorem and solve for x...
15^2 + (x-9)^2 = x^2
225 + x^2 - 18x + 81 = x^2
306 = 18x
x = 17 feet

Answer by It is costly(175)   (Show Source):
You can put this solution on YOUR website!

Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website!
The ladder leans against the building, so the ladder is your hypotenuse.
The height of the building will be one of the legs of the right triangle and the other leg will be the distance of the bottom of the ladder to the building Using Pythagoras' Theorem:
15^2+(h-9)^2= h^2
225+(h-9)^2= h^2 Factor the left:
h^2-18h+306= h^2 Subtract h^2 from both sides:
-18h+306= 0 Rearrange elements:
306-18h= 0 Now factor the left:
-18(h-17)= 0 Divide both sides by -18 (zero divided by any number = 0)
h-17= 0 Add 17 on both sides:
h= 17 is the length of the ladder, your hypotenuse.
And the height of the building is: 17-9= 8-
So we have a triangle with:
Long leg: 15 (distance from the bottom of the ladder to the building)
Short leg: 8 (hypotenuse minus 9)
Hypotenuse: 17
J

Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!
let
the length of the ladder be
the distance from the ground to the top of the ladder
the distance from the bottom of the ladder to the building

if the distance from the ground to the top of the ladder is is less than the length of the ladder , we have

if the distance from the bottom of the ladder to the building is , we have