slope, m, is equal to the ratio between the change in y and the change in x
[tex]m = \frac{\Delta y}{\Delta x} [/tex]
Given:
m ≤ 3/4 (green line in the attached illustration)
Δx = 0.83 ft
Δy represents the height of each step (red lines in the attached illustration)
[tex]\frac{3}{4} = \frac{\Delta y}{0.83} [/tex]
[tex]\Delta y = \frac{3}{4}(0.83) [/tex]
[tex]\Delta y = 0.6225[/tex]
The height of each step should be 0.6225 ft.
Since the whole staircase measures 9 ft high,
9 ÷ 0.6225 = 14.45
There should be 14.45* steps in the staircase.
*This seems illogical because how can you have a 0.45 step, right?
Since the problems says that the slope CANNOT exceed 3/4 (it did not say that the slope is EQUAL to 3/4), we may change the slope of the line such that we will get an integer for the number of steps.
I worked backwards and found out that using m=60/83 (which is less than 3/4, and thus satisfies the given condition) will give a better result:
[tex]m = \frac{\Delta y}{\Delta x} [/tex]
[tex]\frac{60}{83} = \frac{\Delta y}{0.83} [/tex]
[tex]\Delta y = \frac{60}{83}(0.83) [/tex]
[tex]\Delta y = 0.6[/tex]
The height of each step will be 0.6 ft.
9 ÷0.6 = 15
So, there will be a total of 15 steps in the staircase.
