The required angle is angle CAD, and triangle CAD is right-angled.
DC/MC = sin(54°) as triangle DMC is right-angled.
MC/AC = cos(24°) as triangle AMC is right-angled and angle ACM = 48°/2 = 24°.
No two of the above three triangles are in the same plane.
Strictly speaking, the question doesn't give enough information, as it doesn't define the horizontal plane - it just states that AB is horizontal.