Let's analyze the problem step-by-step: --- # Given Data: - Length of the ladder \( l = 4.8\, \text{m} \) - Distance from the wall to the foot of the ladder \( d 1.\, \textm} \) - ladder makes an angle with the ground \theta = 35^\circ \) --- # Step 1: Find the height \( h \) the ladder reaches on the wall Using the right triangle formed: \[ h = l \sin \theta \] Plug in the known values: \[ h = 4.8 \times \sin 35^\circ \] Calculate \( \sin 35^\circ \): \[ \sin 35^\circ \approx .574 \] Therefore: \[ h \approx 4.8 \times .574 \approx 2.76\, \text{m} \] --- # Step 2: Find the horizontal distance from the foot of the ladder to the base of the wall This is given as \( d = 1.8\, \text{m} \). --- # Step 3: Calculate the angle of the ladder with the ground Since the ladder makes an angle of \( 35^\circ \) with the ground, and the problem confirms this, the primary goal is to verify the stability or evaluate the forces or moments if necessary. --- # Step 4: Find the moment about the base of the ladder to check stability (if required) If the problem involves calculating the force or the normal force, we can analyze moments or forces at the contact point. --- # Final Answer: **Height the ladder reaches on the wall**: \[ \boxed{h \approx 2.76\, \text{meters}} \] --- If you need further calculations related to forces, moments, or stability, please specify!