Question 1066946: A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 11 foot 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 33 feet.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Helps to draw this:
If the ladder is x, the vertical distance from the ground is x-11 and the other leg, horizontal, is 33, units in feet.
x^2=(x-11)^2+33^2=x^2-22x+121+1089
x^2 cancel
-22x+1210=0
-22x=-1210
x=55 ft, ladder's length
it is a 33-44-55 right triangle, which is 11 x a 3-4-5 triangle
If the ladder is x and the distance from the ground is x-1 and the distance from the building is 3 feet.
x^2=(x-1)^2+3^2=x^2-2x+1+9
x^2 on each side cancel
-2x+10=0
2x=10
x=5 feet ladder
3 feet from building
leans 4 feet up the building
3-4-5 right triangle.
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