Final answer:
The ladder would be approximately 12.81 feet tall.
Step-by-step explanation:
To find the height of the ladder, we can use the Pythagorean theorem. The ladder, the wall height, and the distance between the ladder base and the wall form a right triangle. Using the theorem, we have:
h2 = 82 + 102
h2 = 64 + 100
h2 = 164
h = √164
h ≈ 12.81 feet
Therefore, the ladder is approximately 12.81 feet tall at the top of the wall.
particularly the analysis of forces acting on a ladder resting against a wall. Given that the ladder is considered frictionless where it contacts the wall (the rain gutter), we need to find the magnitudes of the forces on the ladder at the top and bottom. This means evaluating the normal force and the friction force at the base of the ladder, considering the combined weight of the ladder and the person standing on it. By using principles of static equilibrium — specifically, that the sum of all forces and the sum of all torques must be zero for an object in static equilibrium — we can solve for these forces and meet the conditions of equilibrium.