Questions: What is the minimum height the ladder must be to reach the roof? feet

Solution Steps

• The height from the ground to the roof is 9 feet.
• The distance from the base of the ladder to the wall is 3 feet.

The ladder, the height of the wall, and the distance from the wall form a right triangle. We can use the Pythagorean Theorem to find the length of the ladder (hypotenuse).

\[ a^2 + b^2 = c^2 \]

Where:

• \( a \) is the height of the wall (9 feet)
• \( b \) is the distance from the wall (3 feet)
• \( c \) is the length of the ladder

\[ 9^2 + 3^2 = c^2 \] \[ 81 + 9 = c^2 \] \[ 90 = c^2 \] \[ c = \sqrt{90} \] \[ c \approx 9.49 \]

Final Answer