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?

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) (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:

where a and b are the legs of the triangle and c is the hypotenuse

Plug in a=x, b=6, and c=10. Now lets solve for x

Square each individual term

Subtract 36 from both sides

Combine like terms

Take the square root of both sides

Simplify the square root

So our answer is

So the ladder touches the 8 ft mark on the wall
Answer by scarletedwitch(1) (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
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