SOLUTION: A 10-foot ladder is positioned against a wall. The Base of the ladder is 6 feet from the wall. How many feet up the wall is the top of the ladder?

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Question 119178: A 10-foot ladder is positioned against a wall. The Base of the ladder is 6 feet from the wall. How many feet up the wall is the top of the ladder?
Found 2 solutions by jim_thompson5910, scarletedwitch:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We basically have this triangle set up:


Since we can see that the triangle has legs of x and 6 with a hypotenuse of 10, we can use Pythagoreans theorem to find the unknown side.


Pythagoreans theorem:

a%5E2%2Bb%5E2=c%5E2 where a and b are the legs of the triangle and c is the hypotenuse



x%5E2%2B6%5E2=10%5E2 Plug in a=x, b=6, and c=10. Now lets solve for x


+x++%5E+2+%2B+3+6+=+1+0+0 Square each individual term



+x++%5E+2+=+1+0+0+-+3+6 Subtract 36 from both sides


+x++%5E+2+=+6+4 Combine like terms


s+q+r+t+%28++x++%5E+2+%29+=+s+q+r+t+%28+6+4+%29 Take the square root of both sides



x=8 Simplify the square root




So our answer is
x+=+8


So the ladder touches the 8 ft mark on the wall

Answer by scarletedwitch(1) About Me  (Show Source):
You can put this solution on YOUR website!
Hey there!
So, it looks like a pythagorean theorem will work quiet well here, as the ground and the wall should form a right triangle. Best to start off with a picture.
The short leg would be six, as that's how far the ladder is from the wall, and the hyptenuse should be ten, as that's how long the ladder is explained to be. Therefore, the variable, the wall, will be X.
The formula for is thus: a^2 +b^2 = c^2
a=6
b=x
c=10
6^2 +x^2 = 10^2
Next, you follow the Algebraic steps of PEMDAS. With no Parenthesis, we move on to exponents.
36 + x^2 = 100
Remember that the exponent two mean to multiply the number by itself twice, NOT multiple it by two. Next, we multiply or divide, but there is nothing to do that with, so we move on to addition and subtraction.
x^2 = 100 - 36
x^2 = 64
Good, now that x is alone. We square root both sides. That will leave you with two answers, a negative and a positive 8. However, because you can't have a negative measurement, positive eight is the answer.
Answer is 8 Feet