document.write( "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:
\n" ); document.write( "\"+b+=+.5%28cot+10%29+\"
\n" ); document.write( "is that translated corectly to
\n" ); document.write( "\"+b+=+.5%2810%28b%2F.5%29%29+=+2.5+\"
\n" ); document.write( "and
\n" ); document.write( "\"+d+=+.5%2F%28sin+10%29+\"
\n" ); document.write( "to
\n" ); document.write( "\"+d+=+.5%2F%2810%28.5%2Fd%29%29+\"
\n" ); document.write( "= ???
\n" ); document.write( "ok, that is where I got lost.
\n" ); document.write( "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.
\n" ); document.write( "Thank you for your help
\n" ); document.write( "Lynnette
\n" ); document.write( "lynnettemcarter@yahoo.com \n" ); document.write( "
Algebra.Com's Answer #321227 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
if you look at the following diagram, it should help you understand what to do.
\n" ); document.write( "\"*****
\n" ); document.write( "the ramp forms the hypotenuse of a right triangle.
\n" ); document.write( "the base forms the horizontal leg of the right triangle.
\n" ); document.write( "the height forms the vertical leg of the right triangle.
\n" ); document.write( "plug in any number for 2 out of the 3 variables and you'll get the answer you need for the third variable.
\n" ); document.write( "example:
\n" ); document.write( "height = 3 feet
\n" ); document.write( "angle = 10 degrees
\n" ); document.write( "base = height / tan(angle) = 3/tan(10) = 17.01384546 feet.
\n" ); document.write( "-----
\n" ); document.write( "using the numbers you are showing, I would get the following:
\n" ); document.write( "for a height of 3.5 inches and an angle of 10 degrees, the base length would be found using the following formula:
\n" ); document.write( "base = height / tan(angle) = 3.5 / tan(10) = 19.84948637 inches.
\n" ); document.write( "-----
\n" ); document.write( "the length of the ramp would be found using the following equation:
\n" ); document.write( "ramp = height / sin(angle) = 3.5 / sin(10) = 20.15569669 inches.
\n" ); document.write( "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.
\n" ); document.write( "-----
\n" ); document.write( "for a height of 8 inches, the following formulas would be used:
\n" ); document.write( "base = height / tan(angle)
\n" ); document.write( "ramp = height / sin(angle)
\n" ); document.write( "-----
\n" ); document.write( "with 8 inch height and 10 degree angle, you get the following:
\n" ); document.write( "base = 8 / tan(10) = 45.37025456 inches.
\n" ); document.write( "ramp = 8 / sin(10) = 46.07016387 inches.
\n" ); document.write( "-----
\n" ); document.write( "let me know if this answers your question or if you need more.\r
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