Question

What is the height from the ground at which the top of the 12-foot ladder leans against the wall?

Answer 1

To determine the height at which the top of a 12-foot ladder leans against a wall, we can use the Pythagorean theorem. In this situation, the ladder forms a right triangle with the wall and the ground.

Let:
- \( L \) be the length of the ladder (which is 12 feet).
- \( h \) be the height up the wall where the ladder touches.
- \( d \) be the distance from the base of the ladder to the wall.

According to the Pythagorean theorem:
\[
L^2 = h^2 + d^2
\]

Given that \( L = 12 \) feet, we can express this as:
\[
12^2 = h^2 + d^2
\]
\[
144 = h^2 + d^2
\]

To find the height \( h \), we need to know the distance \( d \) from the base of the ladder to the wall. Without this information, \( h \) could be any height depending on the angle at which the ladder is leaning.

If you can provide the distance \( d \) from the wall or the angle at which the ladder is leaning, we can calculate the exact height \( h \). If you're looking for a specific scenario, please specify!