A block of mass m is placed on a wedge of mass m, inclined at an angle $\theta$, to the horizontal the coefficients of friction between the block and wedge, and the wedge and ground, are high enough for both the block and the wedge to remain static. What is the magnitude of the friction force of the ground on the wedge?

Gravity exerts a force mg download on the block, which means that the wedge must exert a force mg upward on the block. Thus, the block exerts a force mg downwards on the wedge, and gravity also exerts a force mg downward on the wedge. Since these forces have no horizontal components, no friction with the ground is necessary to keep the wedge static.