MOON'S DIAMETER WITH A COIN

MOON'S DIAMETER WITH A COIN

What do you need?

A pen and a piece of paper (you don't need a coin)
Some knowledge of:

If some dynamic worksheets are not available, java can be download from: http://www.houspain.com/gttp/salsaj

Carol overlays the Moon with the coin that Hamza is holding. When the distance between Carol and Hamza is 253cm, these circles seem to be equal .
The distance from the Earth to the Moon is 384400 km and the diameter of the coin is 23mm,
what's the Moon's diameter?

How to solve it?

What do we know?

We already have the diameter of the coin, the distance between Carol and Hamza (wich is the distance between “eye” and coin) and the distance from Earth to the Moon (wich is the distance from “eye” to the Moon).

What do we have to find out?

We'd like to work out the Moon's diameter this being twice the radius.

Work out

If you get bogged down, here you have some directions as to how to find the solution:

Draw freehand a geometric picture of the problem situation on your piece of paper. It should be similar to the dynamic applet.
Watch the following dynamic applet… The orange lines are parallel lines (and purple ones as well)

So, we have to use our mathematical knowledge to go on…, what about Thales' theorem? Do you think is it appropiate to use it? Why?
Watch the following dynamic applet and then, look at your drawing. Do you find any similarity?

Put Thales' theorem into practice.
Work out the value of Moon's diameter.
Is your solution possible? (for instance, 500m would be impossible!)

To increase

We suggest you to work out one more exercise.
¿Y si no tuviera la ayuda de Hamza? ¿De qué tamaño tendría que ser la moneda?

To work out the answer, we give you some hints