i have a gate that is 6 foot tall and 12 foot long. if the top left corner of the gate is moved 2 inches away from the post that it is attached to , how many inches will the top right corner of the gate drop?

The tangent of the angle formed in the vertical pole of 6 feet has a tangent equal to ((1/12)/6)=1/72, the same angle is formed by the horizontal frame part with the horizontal line, so the tangent will be the same. Also the tangent of this angle is ((x/12)/12) = x/144. Making the two tangents equal and solving for x we obtain: x = 2 inches.