Question 1193806
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Triangle XYZ has congruent sides (of equal length 8 units, given).


So, this triangle is equilateral and equiangular: each its interior angle is  190/3 = 60 degrees.


ZW is the altitude from the vertex Z to side XY.


In the same time, ZW is the bisector of the angle Z and the median in triangle XYZ.


m∠WYZ = 60°


m∠YWZ = 90°


m∠YZW = 30°


ZW = {{{(8*sqrt(3))/2}}} = {{{4*sqrt(3)}}} = 6.828  (rounded).


WY = half of XY = 8/2 = 4 units.
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All questions are answered.