Build a triangle from Altitudes?

Three line segments (solid lines) intersect at a point. Could they be the altitudes of some triangle? You can use the sliders to set the lengths of the segments. Drag the R, G and B dots to fix the point at which the segments intersect and the angles between the segments. The dotted lines are perpendicular to the altitudes drawn from the points R, G and B. CHALLENGE: given three altitude lengths, locate the vertices and determine the triangle RGB. Can this always be done? Why or why not?