Solution to the exercise of the mountain height using similar triangles.




Measure of the height of a mountain of the Moon.



What do you need?



  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:

Similar triangles.

Exercise.



Estimate the height of a mountain of the moon.

Working out



What do we Know?



In this exercise we only Know the diameter of the moon: 3476 Km. The piece of infomation that we don´t Know, we will find out by using the program SalsaJ for the image processing.

What do we have to find out?



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

Work out.



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

  1. You can download the following photograph if you click on them.
    Monte PicoMonte Piton
                         Monte Pico                                       Monte Piton
  2. With the program SalsaJ open the photo of the previus step.
  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. 3476 Km.
  5. What is the distance from the terminador to the mountain shadow (segment TB)? 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.
  7. What is the length of the mountain shadow (the segment AM).
  8. Calculate the height of the mountain. You remember the following points:
  • The segment overline{AB}approx overline{A´B} because the curvature is negligible, owing to the mountain height is lesser than the radius of the moon.
  • The mountain is near of the terminador to reject the curvature doubleright the segment TB is a straight line.






BM = mountain height (we want calculate it)
OB = radius of the moon (We Know it)
AM = length of the shadow of the moon (we know it)
TB = distance of the mountain to the terminador.


  • You can check your solves of this exercise, you look for the mountain height in internet.



How do we work with the program Salsa J?



We do the follow point for work with Salsa J:

  1. Open the photo of the moon with the program Salsa J.
  2. For write the scale of the photo in the program:
  3. Now, we will messeaure a distance that we need for resolve this exercise.



Solution.



BM = mountain height (we want calculate it)
OB = radius of the moon (We Know it)
AM = length from the shadow of the mountain (we know it)
TB = distance of the mountain to the terminador.


We observe in the figure that the triangles OBT and AMB are similars, because they have two parallel sides (AM & TB are parallel, and OB & BM are parallels), and they have one same angle ( the angles AMB & TBO are the same ). Now, for the properties os similar triangle. we obtain:

MB/MA = OB/TB

We work out the value of MB, and we obtain the mountain height .

 
soluciontraducion1.txt · Última modificación: 24/04/2017 13:13 (editor externo)
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