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Calculate length of tarp needed to extend 12 linear feet (at 0 degrees), but sloping at 25 degrees instead

I need to cover an area with a tarp, but sloping downward to allow rain to run off.

The area to be covered is 12 feet long (ground/linear measurement).

The tarp will start 9 feet above the ground and slope downward at roughly a 25 degree angle.

How much length of tarp will I need to cover the 12 linear feet after adjusting for the slope?

|*tarp starts here, 9 feet up
|**angled down at ~25 degrees
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|__________________________________12 feet of concrete, end of area to be covered

Would be great if you could include the formula too :-) .
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Scott Pletcher
Asked:
Scott Pletcher
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1 Solution
 
d-glitchCommented:
You need at least sqrt(9² + 12²) = sqrt(225) = 15 feet.

A little more to allow for some sag.
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d-glitchCommented:
The angle is the arctan( 9/12) = 36.8 degrees.
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Scott PletcherSenior DBAAuthor Commented:
But I dont want the tarp to come down to the ground ... only as far down as it would go at roughly 22-25 degrees.

So it won't form a triangle -- it will be an open-ended rectangle.

That is, where the tarp ends up after sloping down should still be some feet off the ground, not at ground level.

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|                       |
|                                            |
|                                                                    |--<<-- tarp ends here
|              
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___________________________________


I can tie the tarp to the middle of the pole, it doesn't hv to reach all the way to the ground.
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d-glitchCommented:
If you hold the angle to 25 degrees, the vertical side of the triangle will be

           12 ft * tan(25)  =  12 * 0.466  =  5.66 ft  ==>  9 - 5.66 = 3.34 ft gap


The length of the tarp will be

           12 ft / cos(25)  =  12 / 0.906  =  13.24 ft
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Scott PletcherSenior DBAAuthor Commented:
Thank you so much!!
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Scott PletcherSenior DBAAuthor Commented:
Hmm, that doesn't really seem right, esp. since the cos(25) is 0.9912, not 0.906 as stated.

However, I did find another web site that had a calculator to properly determine the length.
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Scott PletcherSenior DBAAuthor Commented:
Sorry, your proposed solution to me just didn't hold up as accurate :-( .
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d-glitchCommented:
>> ScottPletcher please recheck you calculator!!!

cos( 25 degrees) does equal 0.906

cos( 25 radians) is 0.9912

25 radians means you go around a circle almost exactly four time.
The effective angle is -1.2 degrees.
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d-glitchCommented:
Where is this calculator website??
And what did it give for an answer??

Was it actually different from the one I gave??
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Scott PletcherSenior DBAAuthor Commented:
Oops, you are quite right as to the COS().

However, I still think the overall formula and result are wrong.

The side being determined is the hypotenuse.  If one side is 12 ft and the other is 3.34 ft, the hypotenuse should be sqrt(12^^^^2 + 3.34^^^^2) which is 12.46 (even I know sqrt of (a^2 + b^2) :-) ).

I can't find any calculation that yields a tarp length of over 13 ft with a linear distance of 12 ft and an angle less than or equal to 25 degrees.

Perhaps you can correct me:

linear distance (12 ft)
--------------------------------------------------------------
---<<--25 degree angle
--tarp
--------extending
-------------------at 25 degrees
-----------------------------------forming a right triangle with the upper edge of the concrete  
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d-glitchCommented:
The gap between the end of the tarp and the ground is 3.34 feet.
This is not part of the triangle.

The sides of the triangle are 12 and 5.66

                  sqrt(12² + 5.66²) = sqrt(144 + 32.04) = sqrt(176.04) = 13.24 feet.
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Scott PletcherSenior DBAAuthor Commented:
Yep, that makes more sense.

Sorry about that, I need to get the q re-opened and then assign you the pts.

I've already ordered the tarp, will probably have to cut down the angle to make it cover all the way :-) .
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d-glitchCommented:
No problem.
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