the triangle in the plan. the give right side is 8000mm =8 metres mate bottom angle is 29 deg top rght angle 112deg top left 39 deg and left length is 11.78647783 Metres top length is 6.16296 metres
the triangle in the plan. the give right side is 8000mm =8 metres mate bottom angle is 29 deg top rght angle 112deg top left 39 deg and left length is 11.78647783 Metres top length is 6.16296 metres
These number look (I didn't calculated) good if I take a quick look. however there is NO way in mathematic hell you could find these value using MATH. You had to use your protractor or some other bloody device.
if we draw a perpendicular line from "the long side" to the upper right corner of the triangle, and our given distance is "A" we split the long side into two triangle bases. the larger one has length:
B = Acos(29°), and the length of the line we drew to make 2 right triangles has length:
C = Asin(29°)
we also know that C = Dsin(39°), where D is the length of the third side (the "top side") of our original triangle. we now know enough to find D, it is:
D = Asin(29°)/sin(39°).
having found D, we can calculate the "short part" of the "long side" of the triangle, it is:
E = Dcos(39°).
the long side of our original triangle thus has length B+E.
since we know the 2nd angle, the upper-right angle is easy to find, it is: 180 - 39 - 29 = 112°.
the length B+E is the one you want to locate the coordinates of the front-left corner of the building, since then you know it is B+E in the direction of 86° (counter-clockwise) from "north" (almost, but not quite, due west).
this is (B+E)cos(86°) meters north, (B+E)sin(86°) meters west (the "west" component will be most of this, the "north" component will be fairly small).
well it looks as if the calculations you have displayed are based on a "big angle" of 100.13° and not 112°. this changes things a LOT (it makes the 3rd angle 50.87° and NOT 39° as you reported)
calculating i get:
B = 8cos(29°) = 6.997 m
C = 8sin(29°) = 3.878 m
so D = (3.878)/sin(50.87°) = 5 m
so E = 5cos(50.87°) = 3.155 m
thus B+E = 6.997 + 3.155 = 10.152 m <--this answer agrees with what you show in your attachment.
the coordinates of the front-left corner are thus:
(10.152cos(86°),10.152sin(86°)) = (0.708 m north, 10.127 m west) which is what is shown.
pro tip: if you are going to use a measuring device to measure something, (like a protractor to measure an angle) measure the biggest thing you can, so that the accuracy of the measuring device contributes less error to your final answer.