Please consider the attached figure, given any acute where and are three altitudes from the vertices and . And is the triangle's orthocenter. Also let , and . Also note that and .

By definition, we have

Consider the right triangle , we have , which implies that

Now consider the two right triangles and , we have and , hence

Also

From here, let's consider the right triangle , we have:

. But , we then have

which implies that

Use the quantities we obtained for and , we have