Question 468155
if you look at the following diagram, it should help you understand what to do.
<img src = "http://theo.x10hosting.com/problems/ramp_1.jpg" alt = "***** picture not found *****"/ >
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.
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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.
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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.
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for a height of 8 inches, the following formulas would be used:
base = height / tan(angle)
ramp = height / sin(angle)
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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.
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let me know if this answers your question or if you need more.