Question

1. a 12-m ladder leans against the wall of a house. the top of the ladder reaches a window 10.5 m above the ground. calculate the distance from the base of the ladder to the wall of the house.

Explanation:

Step1: Identify the right triangle

The ladder, wall, and ground form a right triangle. Let the ladder length (hypotenuse) be \( c = 12 \, \text{m} \), the height on the wall (one leg) be \( a = 10.5 \, \text{m} \), and the distance from the base to the wall (the other leg) be \( b \). We use the Pythagorean theorem: \( a^2 + b^2 = c^2 \).

Step2: Rearrange the formula to solve for \( b \)

\( b^2 = c^2 - a^2 \)
Substitute \( c = 12 \) and \( a = 10.5 \):
\( b^2 = 12^2 - 10.5^2 \)
\( b^2 = 144 - 110.25 \)
\( b^2 = 33.75 \)

Step3: Take the square root to find \( b \)

\( b = \sqrt{33.75} \approx 5.81 \, \text{m} \)

Answer:

The distance from the base of the ladder to the wall is approximately \( 5.81 \, \text{m} \).