A wheelchair ramp with a length of 122 inches(top of ramp) and has a horizontal distance of 120 inches(bottom of ramp):
a) what is the ramp's vertical distance(x)?
b)Construction laws are very specific when it comes to ramps. Each vertical rise of 1 inch requires a horizontal run of 12 inches. Does this ramp satisfy the requirement? Justify your answer.
a) Alright, buckle up for some vertical distance calculation! Now, since we have a horizontal distance of 120 inches and a top height of 122 inches, let's subtract the bottom from the top to find the vertical distance. So, x = 122 inches - 120 inches. And the answer is... *drumroll*... 2 inches! Ta-da!
b) Ah, the construction laws are as precise as a tightrope walker! Here's the deal: the requirement states that for every 1 inch of rise, we need a horizontal run of 12 inches. In our case, the vertical distance is 2 inches. So, is our ramp up to code?
Well, if the vertical distance is 2 inches, then according to the requirement, we should have a horizontal run of 2 inches multiplied by 12 inches. And what's 2 multiplied by 12? It's 24! So, our ramp should have a horizontal run of 24 inches. But, alas, our ramp's horizontal distance is 120 inches. Oopsie!
So, it seems our ramp doesn't meet the construction requirement. It falls short by a whopping 96 inches. The construction laws will have to give this ramp a big thumbs-down. Better luck next time, ramp!
To find the vertical distance (x) of the wheelchair ramp, we'll use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
In this case, the horizontal distance is 120 inches, and the length of the ramp is 122 inches. We can assume that the vertical distance (x) is the missing side we are trying to find.
a) To find the vertical distance (x), we can set up the equation as follows:
120^2 + x^2 = 122^2
Now, let's solve for x:
14400 + x^2 = 14884
x^2 = 14884 - 14400
x^2 = 484
x = √484
x = 22 inches
Therefore, the vertical distance (x) of the ramp is 22 inches.
b) Each vertical rise of 1 inch requires a horizontal run of 12 inches. In this case, the vertical distance (x) is 22 inches, and the horizontal distance (120 inches) is greater than the required horizontal run for this vertical distance (22 inches x 12 inches = 264 inches).
Therefore, according to the construction laws, this ramp does satisfy the requirement because the horizontal distance of 120 inches is larger than the minimum required horizontal run of 264 inches for a vertical rise of 22 inches.
Well, if the triangle formed is of type rectancgle, then what you need to use is Pythagorean theorem. The hypotenuse is 122 inches and one of the cathetus is 120 inches. You clear the other cathetus in the equation and that's it.
a) To find the ramp's vertical distance (x), we will subtract the bottom of the ramp from the top of the ramp.
Vertical distance (x) = Length of ramp at top - Length of ramp at bottom
Vertical distance (x) = 122 inches - 120 inches
Vertical distance (x) = 2 inches
Therefore, the ramp's vertical distance (x) is 2 inches.
b) According to the construction laws mentioned, for every 1 inch of vertical rise, there should be a horizontal run of 12 inches.
Let's check if this ramp satisfies the requirement by calculating the ratio of the vertical distance to the horizontal distance:
Ratio = Vertical distance / Horizontal distance
Ratio = 2 inches / 120 inches
Ratio ≈ 0.0167
Since the ratio is less than 1/12 (0.0833), this ramp does not satisfy the requirement. It means the ramp is steeper than what is recommended by the construction laws.