
Well, let's see. The circumference is 10,900, and that must be π * d.

That means that the diameter is 10,900/π, which is about 3.14.

This gives me a diameter of the moon of about 3,470 km.

Now, to calculate this lengthwell, this is something you've done plenty of.

This is a simple tree problem.

We have a right triangle, we have the opposite side, and we want the adjacent side.

In fact, we know that the tangent of this anglethe tangent of this is 0.5 degrees

has to equal the opposite side d, which is 3,470, over the side we want to calculateL.

Now we can massage this equation a little bit,

bring L up and tangent down

and plug this into our calculator,

and we get an answer of 398,000 km.

This is really amazing what we've done.

I mean, you've learned a little bit of trig and geometry

and from that you've calculated the size of the earth, the size of the moon,

and the distance between the earth and the moon. That's really impressive.