# Math Help - TRIPODing along...

1. ## TRIPODing along...

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)?

2. Originally Posted by Wilmer
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)?
It's not clear to me what sort of "expression" you want for the new height.

The original height h can be calculated in terms of a, b and c. I get the relation $h^2 = a^2 - \frac{b^4}{4b^2-c^2}$. 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 $k^2 = a^2 - \frac{c^4}{4c^2-b^2}$. You could then derive a (messy) expression for the ratio k/h if that is what you wanted.

3. Hello Wilmer,
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
C a

Using the cosine rule the angle between a and A can be determined. If this angle is K h =asinK

bjh

4. Merci BJ.

5. Originally Posted by bjhopper
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
C a

Using the cosine rule the angle between a and A can be determined. If this angle is K h =asinK
Another method is to say that the sphere of radius $a$, centred at the top of the tripod, contains all three vertices of the triangle and hence contains its whole circumcircle. If the radius of the circumcircle is $r$, you then have a right-angled triangle with sides $a$ (hypotenuse), $r$ and $h$. I used the formula for the circumradius, together with Pythagoras, to get the expression for $h$.