How to find Latitudes and Longitudes of projections of the vertices of a rectangular plane below earth's surface?

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I want to find out the latitudes and longitudes of projections of the vertices of a rectangular plane inside the earth's surface. I know dimensions of rectangle, angles of orientation and latitude and longitude of the projection of the center of the rectangle. please help. Earth's curvature is also to be considered

I added an Image which is a 2D representation of what i want. The plane actually is having 2 angles (its trace makes an angle 'A' with North and the plane makes an angle 'B' with the horizontal). I want to find lat longs of all 4 projections

enter image description here