The ratio of the length of the base of a regular triangular prism ABC A1B1C1 to the height of the prism = 0.75.

The ratio of the length of the base of a regular triangular prism ABC A1B1C1 to the height of the prism = 0.75. A plane is drawn through the vertices A and B1 and the middle M of the CC1 edge. Find the sine of the angle between the AC edge and the AMB1 plane.

ABC A1B1C1 is a regular triangular prism.

h = 0.75.

Planes AB1M and AB1K are the same.

SC = a.

MS is the middle line of triangle BB1K.

СР – height.

Hence, BC = SK.

MS = H / 2 /

H = 4 * a / 3;

Hence, MC + H / 2 = 2 * a / 3.

By the Pythagorean theorem, we find:
MK² = (2 * a / 3) ² * a²;

MK = a * √13 / 3 = √13 / 3 * a;

CP = 2 * a / √13 = 2 / √13 * a;

sin PAC = CP / AC = 2 / √13.