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## Homework Statement

Find the center of mass of a triangle with two equal sides of length a. The triangle's third side is length b and it has a uniform mass of M.

## Homework Equations

[itex]R = \frac{1}{M} \int dm \vec{r}[/itex]

[itex]dm = \frac{M}{A}[/itex]

[itex]A = \frac{1}{2}base*height[/itex]

## The Attempt at a Solution

Right now I have my triangle set up with one of the "a" length sides on the x-axis. I'm having trouble defining the y limit in the integral:

[itex]X = \frac{1}{M} \rho \int_{0}^{a} x dx \int dy[/itex]

I know that it has to have length "b" for the triangle I have drawn. I also found that it was equal to tan[itex]\theta_{1}[/itex], but I need it in terms of x to complete the integral. It's that or change variables. I've also been throwing around the idea of doing this in polar coordinates.