SOLUTION: The base of a ladder is 14 feet away from the wall. The top of the ladder is 17 feet from the floor. Find the length of the ladder to the nearest thousandth.

Question 93032: The base of a ladder is 14 feet away from the wall. The top of the ladder is 17 feet from the floor. Find the length of the ladder to the nearest thousandth.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
This is a Pythagorean theorem problem, because a right triangle is formed.
.
The wall is presumed to be perpendicular to the floor. When you lean a ladder against
the wall, the ladder is opposite the right angle formed by the wall and the floor. Therefore,
the ladder is the hypotenuse of the triangle.
.
The distance measured from the intersection of the floor and the wall and up the wall to
the point where the ladder touches the wall (given as 17 ft) is one leg of the right
triangle.
.
And the distance measured from the intersection of the floor and the wall and along the
floor to the point where the ladder rests on the floor (given as 14 ft) is the other leg
of the right triangle.
.
The Pythagorean theorem says that if you square the two legs and add these squares,
the result is equal to the square of the hypotenuse. (Don't forget, the hypotenuse
is the length of the ladder. Call it L.)
.
In equation form this becomes:
.

.
Doing the squares of the numbers makes the equation:
.

.
adding the numbers on the left side:
.

.
Solve for L by taking the square root of both sides to get:
.

.
Rounding to the nearest thousandth results in the length of the ladder being 22.023 feet.
.
Hope this helps you to work your way through the problem. I presume you are allowed to
use a calculator to find the square root of 485 ...
.
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