## Geometry: Common Core (15th Edition)

$\frac{n}{a} = \frac{a}{c}$
All three triangles are similar to one another, meaning that the sides of the triangles are proportional. We can see that $n$ is the longer leg of the larger triangle formed by the altitude of the large triangle, and $a$ is the hypotenuse of that same triangle. Additionally, $a$ is the longer leg of the large triangle. What we want is the corresponding hypotenuse of the large triangle, which is represented by $c$. The proportion should read: $\frac{n}{a} = \frac{a}{c}$