Step 1: Identify the lengths involved. The ladder is 10 meters long (hypotenuse) and the height of the window is 8 meters (opposite side).
Step 2: Use the sine function to relate the angle of elevation (θ) to the opposite side and the hypotenuse. The formula is sin(θ) = opposite/hypotenuse.
Step 3: Substitute the known values into the formula: sin(θ) = 8/10.
Step 4: Simplify the fraction: sin(θ) = 0.8.
Step 5: To find the angle θ, use the inverse sine function: θ = arcsin(0.8).
Step 6: Calculate the angle using a calculator: θ ≈ 53.13 degrees.
