Find The Height Math Question?

see below

AB = BC = AC = 2x12 = 24

those are equilateral triangles, so 

BE = √(24² – 12²)

BE = 12√(2² – 1²) = 12√3

EF = 12 + 12√3 = 12(1+√3)

EF is h/2 from symmetry

h = 24(1+√3) = 65.57 aprox.

2equi tri +24

sin(60)=.866*12

=24+(12*.866)*4=65.568

Hint:

Centres A(top circle)  , B , C(bottom circle) , DABCD is a rhombus , ABD is an equilateral side 24

--> AC = ...

and

h = ...