Math CentralQuandaries & Queries


Question from Maura, a student:

I am trying to calculate the height of an isoceles triangle but in this case AB is not equal to AC.
How do I calculate this?

Thank you,

Maura age 13

Hi Maura.

It sounds like the isosceles triangle is lying on its side then. So BC = AC (or BC = AB, it doesn't matter which, but I'll just say BC = AC for the sake of argument).

So you want to know the height from A down perpendicularly to the line containing BC.

Let's say you rotated it so that AB is on the bottom and C is the vertex at the top, so the height is from C down to AB. From the wording of your question, I think you already know how to solve this problem: the height can be calculated by dividing the length AB by two, then using that with the hypotenuse AC in a right triangle through Pythagoras' Theorem to find the height. Nothing is stopping you from doing just that right now, I presume.

The reason this isn't just a wild goose chase is that knowing the height and the base means you know the area of the triangle, right? And the triangle's area is going to be the same for any chosen base and height. So calculate the area, then use the length AB together with the area to find the height from A down to BC!

There are other ways to solve the problem too, but I thought you'd appreciate this method.

Neat question!
Stephen La Rocque.

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS