From point M, a rectangle ABCD is drawn perpendicularly MD = 4cm to the plane, oblique MA and MC

From point M, a rectangle ABCD is drawn perpendicularly MD = 4cm to the plane, oblique MA and MC form a plane triangle with an angle of 45 and 30, respectively. Find the sides are rectangular.

Since the segment MD is perpendicular to the plane of the rectangle, then MD is perpendicular to AD and CD, and then triangles ADM and CDM are rectangular.

The ADM triangle is rectangular and isosceles, since the angle is DAM = 45, then AD = MD = 4 cm.

In a right-angled triangle CDM tg30 = MD / CD.

СD = МD / tg30 = 4 / (1 / √3) = 4 * √3 cm.

Answer: The sides of the rectangle are 4 cm and 4 * √3 cm.