Question

Xyz is an isosceles triangle with XY=xz=6cm and YXZ=120° calculate the length of YZ

Answer 1

draw altitude from X to A at the center of YZ

Then angle YXA = 120/2 = 60
then angle at Y = angle at Z = 30 to make XAY a 30 60 90 triangle
XA= 6/2 = 3 the altitude because sin 30 = 1/2
then
YA^2 = 36 - 9 = 27
so YZ = 2 sqrt 27
about 10.4 cm