A building code regulation requires that the slope of the riser to the tread of a staircase be 60% with an absolute deviation of 10%. Find the maximum and minimum slopes of the staircase.
To find the maximum and minimum slopes of the staircase, we need to consider the regulation which states that the slope of the riser to the tread should be 60% with an absolute deviation of 10%.
The slope of the riser to the tread is calculated by dividing the vertical rise (height) of the riser by the horizontal depth (tread) of the step.
Let's assume that the height of the riser is represented by 'h' and the tread depth is represented by 't'.
According to the building code regulation, the slope of the riser to the tread should be 60% or 0.60. Thus, the slope can be expressed as:
Slope = h/t = 0.60
Now, let's incorporate the absolute deviation of 10% into the equation. The absolute deviation allows for a variation of ±10% from the specified slope of 60%.
Maximum slope:
To find the maximum slope, we need to increase the slope by 10%. Therefore, the slope can be written as:
Slope = (0.60 + 10% of 0.60) = 0.60 + 0.10*0.60 = 0.60 + 0.06 = 0.66
Minimum slope:
To find the minimum slope, we need to decrease the slope by 10%. Therefore, the slope can be written as:
Slope = (0.60 - 10% of 0.60) = 0.60 - 0.10*0.60 = 0.60 - 0.06 = 0.54
Therefore, the maximum slope of the staircase is 0.66 or 66%, and the minimum slope is 0.54 or 54%.