In all of your problems you are dealing with a specific kind of right triangle: one where the two legs are equal. So

<-- Since y = x

If you are given one of the legs, you know the other one is equal to the given leg. If you are looking then for z then solve the above equation for z.

If you are given z then you know the two legs are equal and equal to x in the above equation. So solve it for x.

Example: You are given y = 5. Thus x = y = 5. And

.

Example: You are given z = 20. Thus

(Which simplifies to .)

Doing the other kinds of triangles involves a similar process, though, of course, x and y may not be equal. Either way we still have and you can work from there.

-Dan