Find offset point of triangle

Question

I need to find the offset distance of 2 points.

I start with my basic shape

The dashed lines are help lines

https://snipboard.io/VldCM6.jpg

Now I will offset the line and need to find point X and Y

https://snipboard.io/F6WtyG.jpg

Since I only know the offset and nothing else I wonder how to continue from here

Answer 1

A.  Ridge Offset:

Offset determined by similar triangles.  Use the large triangle as diagramed in your attachment (LL=57.15, SL=24, HYP=61.98) and a small ridge triangle with additional construction lines (see graphic solution below).  You are solving for the hypotenuse CJ of the smaller triangle, the required ridge offset. 

 61.98/CJ = 57.15/3.5

57.15(CJ) = 3.5(61.98)

57.15(CJ) = 216.95

      ∴  CJ = 3.80

For Ridge Offset diagram, see......

https://snipboard.io/DF5eAs.jpg

B.  Eave Offset:

Construct additional lines to determine the required angles for a strategically selected triangle using given information from your diagram (see graphic solution below).  The selected triangle AHM (LL=3.5, β=33.61°) is used to calculate the short leg MA (or HI using triangle AHI), the required offset dimension using trigonometric properties.

TAN(33.61°) = (side opp) / 3.5

TAN(33.61°) = MA / 3.5

         0.66 = MA / 3.5

          MA = 0.66(3.5)

     ∴  MA = 2.33

For Eave Offset diagram, see......

https://snipboard.io/SWsVGY.jpg