Measure the height of the mountain in the not illuminate zone of the moon.

1. Paper and pen.
2. The program Salsa J (you can download this program in this page. http://www.houspain.com/gttp/salsaj) for the image proccesing.
3. Knowledge of:

• Equation of second degree.
• Pythagorean Theorem.

Estimate the height of a mountain of the moon.

In this exercise we only Know the diameter of the moon, 3476 Km. The other dates that we´ll need for we solve the exercise, we will find out by using the program SalsaJ for the image processing.

The objective of this exercise is to Know the height of the mountains of the moon by using mathematics.

You will can solve this exercise if you do the following points:

1. You can download the following photograph if you click on them.
   
2. With the program SalsaJ open the photo of the previus point.
3. In the photo, the blue circles show the mountains that you can study.
4. We have to write the scale of the photo in the program SalsaJ, for this we only need to Know the diameter of the moon.
5. What is the distance between the terminador and the tip of the mountain (the segment A´B´)?. Terminador is the line that differentiate the illuminate zone of the not illuminate zone of the moon.
6. We know the radius of the moon, because we know the diameter of the moon: 3476 Km.
7. Identificate, in the figure of the point 10, one right triangle.
8. In the right triangle of the previus point, apply the Pythagorean theorem.
9. Rename the segments with letters (you look the next point).
10. Calculate the height of the mountain with a second degree equation. For your need, look the next figure:

• How we get the following figure?

A´= the tip of the mountain.
A´B´= d = the distance between the tip of the mountain and the terminator.
AA´= a = the height of the mountain
OA = R (ratio of the Moon)


NOTA: the result will be in function of R and d.