Trapezoid have 4 length side lines
Now find proportions
Find height of trapezoid
Divide trapezoid in 1 rectangle and 2 triangles
Then , the 2 triangles have a base of (23-15)/2 = 4
Then height is 4 x WZ x sin 56
Angle Z = (180-56-90) + 90 = 124 degrees
Angle X = 360-124- 56 - 121= 59 degrees
Now look at line 23
Then WZ• cos56 + 15 + XY• cos 59 = 23
Now if both angles Z and Y were similar ,then
TR would be (WX + ZY )/2, because T divides half WZ
BUT theyre not similar, theres a little difference . Then find this difference
Use formula cos (a+b) = cosa• cosb- sina•sinb
then
cos 59 = cos56• cos3 - sin56•sin3
aproximate cos3= 1 , sin3=0
then WZ• cos56 + XY•cos 56 + 15 = 23
(WZ + XY)•(cos56) = 23-15= 8:
(WZ + XY) = 8/(cos56) = 14.285
(WZ + XY)/2 =7.1428
then TZ = 7.1428/2 =3.5714
Finally TR = 15 + 2•TZ cos 56 = 18.994