A tripod has equal length legs = a.
It sits on an isosceles triangular base, sides b,b,c.
It has height = h.
If the base is changed to sides b,c,c, what is the new height (as an expression)?
The original height h can be calculated in terms of a, b and c. I get the relation . If the sides of the base are changed from b,b,c to b,c,c, that is equivalent to exchanging b and c. So the new height k would be given by . You could then derive a (messy) expression for the ratio k/h if that is what you wanted.
Creating an expression is too messy for me but given a,b,c the triangle which determines the altitude h consists of the following line segments
A perpendicular bisector of base triangle bbc
B perpendicular bisector of tripod triangle aac
Using the cosine rule the angle between a and A can be determined. If this angle is K h =asinK
formula for the circumradius, together with Pythagoras, to get the expression for .