Pythogorean thorem: Find distance of ladder from house

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jshaziza

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Jan 26, 2007
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A 13 foot ladder is leaning against a house.The distance from the bottom of the ladder to the house is 7 feet less than the distance from the top of the ladder to the ground. How far is the bottom of the ladder from the house?

I've done these kind of questions in Geometry before but I forgot the complete method I used. Like I know I would use the pythogorean thorem to solve this and that the hypotenuse is the 13, the leg from the bottom of ladder to the house is represented by x-7, but I am not sure if I should also designate the other leg as x. So if someone could refresh my mind with the correct formula that would be great. Thx.
 
Yep, you just use x for the other leg.

x^2 + (x - 7)^2 = 13^2

And solve the quadratic equation.
 
It can't be right though because when I solve this equation I come up with x=about 7.7.
x^2+(x-7)^2=13^2
x^2 +x^2+49=169
2x^2+49=169
2x^2=120
x^2=60
x=about 7.7

Now that I have that 7.7-7=0.7

7.7^2+ 0.7^2=x^2
59.29+0.49=x^2
59.78=x^2
x=about 7.7

It should equal 13 so I know it must be wrong. If I am doing something wrong please point it out. Thx.
 
jshaziza said:
It can't be right though because when I solve this equation I come up with x=about 7.7.
x^2+(x-7)^2=13^2
x^2 +x^2+49=169
2x^2+49=169
2x^2=120
x^2=60
x=about 7.7

Now that I have that 7.7-7=0.7

7.7^2+ 0.7^2=x^2
59.29+0.49=x^2
59.78=x^2
x=about 7.7

It should equal 13 so I know it must be wrong. If I am doing something wrong please point it out. Thx.
Click to expand...

Ummmm.....

Let x = distance from top of the ladder to the ground (vertical distance)

Then x - 7 = distance from the point on the ground at the bottom of the wall to the foot of the ladder.

You should definitely draw a diagram for this.

Now, use the Pythagorean theorem. The length of the ladder is the hypotenuse of a right triangle which has legs of x and x - 7.

x<SUP>2</SUP> + (x - 7)<SUP>2</SUP> = 13<SUP>2</SUP>

x<SUP>2</SUP> + (x<SUP>2</SUP> - 14x + 49) = 169

Ok...now, YOU solve this for x....
 
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