To find the length of the ladder needed to reach the window, we can use the Pythagorean theorem. The ladder, the distance from the base of the window to the base of the ladder, and the height of the window form a right triangle.
- Let:
- \( a \) = the height of the window = 7 feet
- \( b \) = the distance from the base of the window to the base of the ladder = 24 feet
- \( c \) = the length of the ladder (the hypotenuse)
According to the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
- Substitute the known values into the formula:
\[ c^2 = 7^2 + 24^2 \] \[ c^2 = 49 + 576 \] \[ c^2 = 625 \]
- Now, take the square root to find \( c \):
\[ c = \sqrt{625} = 25 \]
Therefore, the length of the ladder must be 25 feet to reach the window.