Question

a ladoing dock ramp that is 177 feet long risese at an angle of 16.1 degrees from the horizontal. due to new design specifications, a longer ramp is to be used, so that the angle is reduced to 7.2 degrees. how much farther out from the dock will that put the foot of the ramp

Answer 1

Interpretation: the dock height stays the same, the ramp length changes so the incline drops from 16.1° to 7.2°. Let the original ramp length L = 177 ft.

1. Height of the dock (vertical rise):
h = L sin(16.1°) = 177·sin(16.1°) ≈ 49.08 ft.

2. Horizontal distance of original ramp:
x1 = 177·cos(16.1°) ≈ 169.65 ft.

3. Horizontal distance with new angle (same h):
x2 = h · cot(7.2°) = h · (cos7.2°/sin7.2°) ≈ 388.89 ft.

4. Increase in horizontal distance:
x2 − x1 ≈ 388.89 − 169.65 ≈ 219.24 ft.

Answer: about 219.2 feet farther out (≈ 219 ft).