SOLUTION: Given: â–³XYZ with XY ≅ XZ ≅ YZ ZW ⊥ XY with W on XY YZ = 8 Find: ZW Find the measures of the following angles in degrees. m∠WYZ = ° m∠YWZ = ° m∠YZW = Â

Algebra ->  Formulas -> SOLUTION: Given: â–³XYZ with XY ≅ XZ ≅ YZ ZW ⊥ XY with W on XY YZ = 8 Find: ZW Find the measures of the following angles in degrees. m∠WYZ = ° m∠YWZ = ° m∠YZW =       Log On


   

Question 1193806: Given: △XYZ with XY ≅ XZ ≅ YZ ZW ⊥ XY with W on XY YZ = 8
Find: ZW
Find the measures of the following angles in degrees.
m∠WYZ =
°
m∠YWZ =
°
m∠YZW =
°
Find WY.
WY =
Find The simplest radical form of simplest radical form ZW
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

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 = %288%2Asqrt%283%29%29%2F2 = 4%2Asqrt%283%29 = 6.828  (rounded).


WY = half of XY = 8/2 = 4 units.

All questions are answered.