A ladder measuring 13 feet is leaning against a house. If the distance from the base of the ladder to the house is 5 feet, how high does the ladder reach?

To determine how high the ladder reaches on the wall of the house, we can utilize the Pythagorean theorem. The situation can be visualized as a right triangle where the ladder acts as the hypotenuse, the distance from the base of the ladder to the house is one leg, and the height the ladder reaches on the wall is the other leg.

In this scenario, let:

• The length of the ladder (hypotenuse) = 13 feet,

• The distance from the base of the ladder to the house (one leg) = 5 feet,

• The height reached on the wall (the other leg) = ( h ).

According to the Pythagorean theorem:

[

a^2 + b^2 = c^2

]

where ( c ) is the hypotenuse, and ( a ) and ( b ) are the other two legs.

Substituting the known values into the equation gives:

[

5^2 + h^2 = 13^2

]

Calculating the squares:

[

25 + h^2 = 169

]

To solve for ( h^2 ), subtract 25 from both sides:

[