In the figure below SolutionTriangle ABC IS A 306090 special

Solution

Triangle ABC IS A 30-60-90 special triangle

And in 30-60-90 triangle, hypotenuse= 2 * short leg

short leg , BC= hypotenuse/2 = 4/2=2

Long leg AB= sqrt3 * short leg= 2 sqrt 3

BC +CD=8

In triangle ABD

Hypotenuse AD = sqrt((2sqrt 3)² + 8²) = sqrt 76= 2sqrt19