SOLUTION: a ladder that is 13 feet long is a 5 feet from the base of a wall. How far up the wall does the ladder reach?

Question 113221: a ladder that is 13 feet long is a 5 feet from the base of a wall. How far up the wall does the ladder reach?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
This is a right triangle problem.
.
When you lean a ladder up a wall, a right triangle is formed. The 90-degree angle of this
right triangle is at the base of the wall and the sides of this angle are the vertical
wall and the horizontal ground. Since the hypotenuse of a right triangle is the longest side
and is the side opposite to the 90-degree angle, the leaning ladder is the hypotenuse
of the triangle. One leg of the right triangle is the distance along the ground between the
bottom of the ladder and the base of the wall. The other leg of the triangle is the distance
up the wall from the base of the wall to the point where the ladder is leaning on the wall.
.
The Pythagorean theorem applies to right triangles. This theorem states that the square of the
hypotenuse of a right triangle is equal to the sum of the squares of the two legs.
Call H the hypotenuse, A one of the legs, and B the other leg of the triangle. So in equation
form the Pythagorean equation is:
.

.
For this problem you are told that the ladder (the hypotenuse) is 13 feet long and one of
the legs (the distance from the bottom of the ladder to the wall) is 5 feet. Substituting
these values into the equation results in it becoming:
.

.
Square out the numbers and you have:
.

.
Subtract 25 from both sides to get rid of the 25 on the right side and the equation
reduces to:
.

.
Solve for B by taking the square root of both sides of this equation and you have:
.

.
B is the other leg of the triangle, so it is the distance up the wall from the ground to the
point where the ladder is resting on the wall. That distance is 12 feet.
.
Hope this helps you to understand the problem a little better and provides you with an
understandable method that you can use to solve it.
.
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