Elementary Geometry for College Students (7th Edition)

So $HL= 6$ $HK = 12$ $MK= 6$
In $\triangle HKL$ $\angle HKL = 30^{\circ}$ So $\angle LHK =60^{\circ}$ now By Theorem 5.5.2/ (30-60-90 Theorem) $LK= 6\sqrt 3$ given So $HL= 6$ $HK = 12$ $MK= HK/2 = 12/2= 6$