The minimum value of the sum of the lengths of the hypotenus
The applet allows to investigate the task : Finding angles of two right-angled triangles for which the sum of the lengths of the hypotenuses is minimum.
The two right-angled triangles and are shown. In addition, there are three variation slide bars: a slide bar along the leg , a slide bar along the leg , and a slide bar t for the sum of the legs . When the vertex C is dragged, the location of the vertex changes in accordance with the sum of the legs .At any stage the following values appear on the screen: the sums of the lengths of the hypotenuses of the triangles , and the magnitudes of the angles and . The minimum the minimum value of the sum of the lengths of the hypotenuses, is obtained when the triangles are similar.