SOLUTION: Please help me find the length of the base and diagonal for 2 handicap ramps with known heights of 3.5" and 8" and a max slope of only 10 degrees. I tried using .5 feet to work out

Question 468155: Please help me find the length of the base and diagonal for 2 handicap ramps with known heights of 3.5" and 8" and a max slope of only 10 degrees. I tried using .5 feet to work out the algebra in the geometric equation. I believe I need to use the following:

is that translated corectly to

and

to

= ???
ok, that is where I got lost.
Honestly this is not Homework, but Housework. Trying to build ramps that my 80 year old mother can use to access the levels in her home in a wheel chair.
Thank you for your help
Lynnette
lynnettemcarter@yahoo.com
Found 3 solutions by ccs2011, Theo, stanbon:
Answer by ccs2011(207)   (Show Source): You can put this solution on YOUR website!
First I will give solution in general terms then plug in known heights of 3.5" and 8".
Let b,h,d be base,diagonal, and height of the ramp
Let A be the angle, where A < 10
Using trig relationships:

Multiply by d on both sides

Divide by sin A on both sides

***********************

Multiply by b on both sides

Divide by tan A on both sides

***********************
Now you can substitute a given height and the desired angle.
Use a scientific calculator to obtain trig functions, ex: tan(10) = .1763
For h = 3.5", A = 10 degrees

***************************
For h = 8", A = 10 degrees

Note if you need to decrease the angle, the lengths of b,d will increase
Hope that helps,
good luck with the ramps

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
if you look at the following diagram, it should help you understand what to do.

the ramp forms the hypotenuse of a right triangle.
the base forms the horizontal leg of the right triangle.
the height forms the vertical leg of the right triangle.
plug in any number for 2 out of the 3 variables and you'll get the answer you need for the third variable.
example:
height = 3 feet
angle = 10 degrees
base = height / tan(angle) = 3/tan(10) = 17.01384546 feet.
-----
using the numbers you are showing, I would get the following:
for a height of 3.5 inches and an angle of 10 degrees, the base length would be found using the following formula:
base = height / tan(angle) = 3.5 / tan(10) = 19.84948637 inches.
-----
the length of the ramp would be found using the following equation:
ramp = height / sin(angle) = 3.5 / sin(10) = 20.15569669 inches.
with an angle of only 10 degrees, the difference in the length of the ramp and the length of the base would not be large.
-----
for a height of 8 inches, the following formulas would be used:
base = height / tan(angle)
ramp = height / sin(angle)
-----
with 8 inch height and 10 degree angle, you get the following:
base = 8 / tan(10) = 45.37025456 inches.
ramp = 8 / sin(10) = 46.07016387 inches.
-----
let me know if this answers your question or if you need more.

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Please help me find the length of the base and diagonal for 2 handicap ramps with known hights of 3.5" and 8" and a max slope of only 10 degrees.
----
The 3.5" rise.
------------------
Draw the picture.
You have a right triangle with
rise angle of 10 degrees and side
opposite the 10 degrees = (3/5)/12 = (3/5)(1/12) = 1/20 ft.
-----------------------
To find the length of the hypotenuse (ramp) use:
sin(10 degrees) = (1/20)/ramp
---
ramp = (1/20)/sin(10 degrees)
---
ramp = 0.2879 ft
====================
The 8" rise.
Draw the picture.
sin(10 degrees) = (8/12)/ramp
ramp = (2/3)/sin(10 degrees)
ramp = 3.84 ft
===================
Cheers,
Stan H.
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