A ramp must not rise more than 1 foot over a horizontal distance of 12 feet.

a) What is the maximum slope of the ramp into the house

b) If the horizontal distance into the house is 48 feet, what is the maximum allowable rise of the ramp?

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a) max slope = 1/12

b) rise/48' < 1/12
Solve for the maximum rise

a wedge shaped skate boarding ramp rises to a height of 15 inches over a 35 inches horizontal distance find the slope of the ramp

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To find the maximum slope of the ramp, we need to determine the ratio of the rise (vertical distance) to the run (horizontal distance). In this case, the rise must not exceed 1 foot over a run of 12 feet.

a) Maximum slope of the ramp:
The slope is calculated as the rise divided by the run. In this case, the rise is 1 foot and the run is 12 feet.

Slope = Rise / Run
Slope = 1 foot / 12 feet
Slope ≈ 0.083

Therefore, the maximum slope of the ramp into the house is approximately 0.083.

b) To calculate the maximum allowable rise of the ramp when the horizontal distance into the house is 48 feet, we can use the same ratio of rise to run obtained from part a).

Maximum allowable rise = Maximum slope × Run
Maximum allowable rise = 0.083 × 48 feet
Maximum allowable rise ≈ 3.98 feet (rounded to two decimal places)

Therefore, when the horizontal distance into the house is 48 feet, the maximum allowable rise of the ramp is approximately 3.98 feet.