This plugin adds a processing algorithm that lets you create cast shadows from polygon shapes.
Use the UI Button or the algorithm "Create cast shadow" to open the algorithm window.
Select the input layer.
Define the height field. This could be either the stories of buildings or height in meter. If the height field is kept empty, all shadows just get the same length.
Define the angle of the shadow.
Define the length factor that is multiplied with the height field to create the length of the shadow.