A ramp currently has a length of 24 feet and forms an angle, θ_1 , of 30° with the ground. To comply with new safety standards, the ramp needs to be extended to 40 feet (as illustrated by Ramp 2), while the height of the dock remains unchanged at 12 feet. Adjusting the ramp incurs a cost of $50 per degree of change. What will be the total cost to implement this adjustment?
C
1 dollars comma 200 point 0 0D
2 dollars comma 000 point 0 0The dock height is 12 feet, and the new ramp is 40 feet long, so the new angle is sin⁻¹(12/40) ≈ 17.46°. The angle changes from 30° by about 12.54°, and at $50 per degree the cost is 12.54 × $50 ≈ $627.12. The correct choice is B, $627.12.
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