Tissues can grow in a particular direction by controlling the orientation of cell divisions. This phenomenon is evident in the developing Drosophila wing epithelium, where the tissue becomes elongated along the proximal-distal axis. We show that orientation of cell divisions in the wing requires planar polarization of an atypical myosin, Dachs. Our evidence suggests that Dachs constricts cell-cell junctions to alter the geometry of cell shapes at the apical surface, and that cell shape then determines the orientation of the mitotic spindle. Using a computational model of a growing epithelium, we show that polarized cell tension is sufficient to orient cell shapes, cell divisions, and tissue growth. Planar polarization of Dachs is ultimately oriented by long-range gradients emanating from compartment boundaries, and is therefore a mechanism linking these gradients with the control of tissue shape.