What is the run if the rise is 36 inches over a 60º angle?

Question

I understand that "To find the rise over run for any degree value, you multiply 12 * tan(x) where x is the degrees." but I don't know how to calculate the run over rise. Any assistance would be greatly appreciated to compensate for my poor math ability.

Answer 1

You do use tan(x). Tan(x)=Rise/Run so Run is Rise/Tan(x) which in this case will be Run=36/Tan(60) = 12sqrt(3). This is about 20.78 degrees.

Answer 2

First draw a 30-60 degree right triangle with the short leg in the horizontal position adjacent to the 60 degree angle. We know that the sides of a 30-60 degree triangle are in the ratio 1,2,sqrt3 with 1 the short leg, 2 the hypotenuse, and sqrt3 the long leg. So we can write run/1 = rise/sqrt3 which is just the ratio of corresponding sides in similar triangles. But we are given a rise of 36 so we can write

run/1 = 36/sqrt3 and solve for run to get 12sqrt(3)..

Or, if you know how to get tan60 from a 30-6- right triangle just write

tan(60) = sqrt(3) = opp/adj = 36/run and solve to get

run = 36/sqrt(3) which simplifies to 12sqrt(3)

Answer 3

slope of any line is rise/run. Rise is opposite side and run is adjacent side. Since tan is opposite side by adjacent side, slope or rise/run is equal to tan of angle made by the line with horizontal.

rise/run = tan(θ)

tan(60) = 36/run

36/run = √3 (since tan(60) = √3)

run = 36/√3

multiply with √3/√3

= 12√3

Answer 4

run = 36/√3 = 12√3 in., since run is the horizontal displacement.
Reason: For 30-60-90 special triangle, the longer log = √3 x the shorter leg.
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Ideas to save time: Use special triangle property.