Advanced Math/Length- Supports
QUESTION: A slide of uniform grade is to be constructed on a level surface and is to have 10 supports with equal distances between the supports.
Length of longest support- 42.5 feet
Length of shortest support- 2 feet
Calculate length of each support.
Also, can the approximate length of the slide be calculated if the support lengths were placed end to end and due to being equally spaced?
ANSWER: Since the first support is at the beginning of the slide, the TEN supports divide the slide into NINE sections.
The last support is 40.5 feet taller than the first support.
40.5 ÷ 9 = 4.5 feet
Each support is 4.5 feet taller than preceding one:
support 1: 2 ft
support 2: 6.5 ft
support 3: 11 ft
support 4: 15.5 ft
support 5: 20 ft
support 6: 24.5 ft
support 7: 29 ft
support 8: 33.5 ft
support 9: 38 ft
support 10: 42.5 ft
I'm not sure what you mean by "the support lengths were placed end to end."
To find the length of the slide, you need either the angle of inclination or the distance between supports.
---------- FOLLOW-UP ----------
QUESTION: "the support lengths were placed end to end."
Typo error- should be: The supports were placed end to end.
Note that the heights of the supports are not a function of the length of the slide. The heights were determined by number of supports and the difference in height between the first and last support. Since their heights are constant, their total is constant (222.5 feet), no matter how long the slide.
You can see that the supports are the same heights for both slides, but the shorter slide is steeper.)
Therefore, you cannot determine the length of the slide by measuring the supports. That is why you need either the angle of inclination or the distance between supports.
Suppose you know that the supports are spaced x feet apart.
The first and last supports are 9x feet apart. By the Pythagorean Theorem, the length of the slide is √(81x² + 42.5²) feet.
Suppose you know the angle of inclination but not the spacing of the supports.
Let θ be the angle of inclination and S the length of the slide.
S = 40.5/sinθ