a) To find the angle of elevation, we need to use trigonometry. Let's consider a right triangle, where the vertical rise of each step is the opposite side, the horizontal distance between each step is the adjacent side, and the hypotenuse is the line connecting the first and last step. Let's call the angle of elevation θ. Then we have:
tan θ = opposite/adjacent
tan θ = 15/18
θ = tan⁻¹(15/18)
θ ≈ 41 degrees
Therefore, the angle of elevation is approximately 41 degrees.
b) Following the same steps as before, but now with a vertical rise of 12 inches and a landing of 20 inches, we have:
tan θ = opposite/adjacent
tan θ = 12/20
θ = tan⁻¹(12/20)
θ ≈ 31 degrees
Therefore, the new angle of elevation is approximately 31 degrees.