To find out the length of the ladder that Ms. Upton leans against the wall, we need to use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this problem, the wall and the ground form a right angle, and the ladder forms the hypotenuse of this right triangle.
Let's denote the following:
- The base distance from the wall to the bottom of the ladder as [tex]\(a\)[/tex], which is 5 feet.
- The height from the floor to the point where the ladder touches the wall as [tex]\(b\)[/tex], which is 12 feet.
- The length of the ladder as [tex]\(c\)[/tex], which is the hypotenuse we need to find.
According to the Pythagorean theorem:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
Substituting the known values:
[tex]\[ c^2 = 5^2 + 12^2 \][/tex]
[tex]\[ c^2 = 25 + 144 \][/tex]
[tex]\[ c^2 = 169 \][/tex]
To find [tex]\(c\)[/tex], we take the square root of both sides:
[tex]\[ c = \sqrt{169} \][/tex]
[tex]\[ c = 13 \][/tex]
Therefore, the length of the ladder is 13 feet.
