Build a triangle from Altitudes?

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

Information: Build a triangle from Altitudes?