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MATHEMATICAL OF THE TRIANGLES

SIMPLE “THEODOLITE?

The ojetivo of this experiment is the one to measure the height of the great buildings being used a device that allows to measure Ãngulos.

INTRODUCTION

It imagines that you are visiting Paris, and you wish to know the height of Torre Eiffel Tower. Just by two measures the height of Torre Eifel can be calculated. Flgura 1 of abjo indicates to us how.

Figure 1. How to measure the height of Torre Eiffel Tower.

These measures are based on the mathematics of the triangles rectÃngulos. A good distance is needed the object to make the first measurement. We will assume that you went to a distance of 575 meters of the base of the tower. This distance is the basic lÃnea of triÃngulo rectangle of figura1. The height of the Tower is the vertical side of the triangle. The point from where it is observed is the third side of the triangle (called the ‘hypotenuse’). The second measurement that is needed to do is to measure Ãngulo between the point denode is observed and the ground, that gives to the basic line of the triangle rectangle us. In Figure 1, the angle has been marked with a symbol that is the Greek letter theta. The mathematicians are in favor crazy of the Greek letters and the Theta letter is the one that uses for the angles. In the Experimental part we will see the form to make a clinometer that will allow us to measure the angles. For this example we say that you measured an angle of 29

°.

Good we have the length of the base (575 ms), and angle (29

°). How calculate does the height? Here it enters mathematical of the triangles the rectangles. By definition a triangle rectangle is that one that less than has 90 degrees in a side and the other sides 90 degrees (the sum of the sides of the triangle is always 180 degrees).Figure 2 shows our triangle without Torre Eiffel. The right angle brand with a small rectangle, our measured angle is Theta and the remaining angle must be smaller to 90 degrees.

Figure 2. Triangles rectangles and the function of tangent (so)

It is that the Theta angle has special a mathematical relation with the sides to and b. For a given angle, the relation of the length of those two sides is always the same:   a/b is equal to the tangent of the Theta angle, the equation sees asÃí:

a/b = so Theta

Another form to write the same equation is:

a = b * so theta

This means that the height that we wished to measure (a) is equal to the base of the triangle rectangle (b) by the tangent of the angle (Theta). Then the height deberÃa to be: 575 * so (29) = 575 * 0,5543 = 319 M.s

When evriguar the height of Torre Eiffel in the Internet you find out to you that it measures 324 M.s How needs has been your measurement? Good. the difference is of 324 - 319 = 5 meters. The calculation of error gives 5 us/324 * 100 = 1,5%. It is notbadly! A good measurement must be in marge of error of 2%. (It tries to see that it happens with the allowable error if you change 1 degree.)

  • SINCE THE CLINOMETER BECOMES
  • in order to ahacer this equipment simply we will need:
  • 1 great Transporter
  • 1 tube of plastic or cardboard
  • 1 plummet
  • glue

paper

pencil

          SINCE ONE BECOMES
1. - We took the transporter and we do a hole to him to means.
2. - We introduce by the hole the thread of the plummet and make a knot so that one does not leave.
 




Tangents3. - We took the tube and we beat on a flank of this transporter.

In the part down the form can be seen to use this simple theodolite.

EQUIPMENT OF TANGENTS      
This simple equipment us permitiá automatically to calculate the height of a building, post of public lighting system or tree by means of trigonometry. Ideal to make demonstrations of mathematics. (Beam click in the photo for a greater image)

-    Price SU$ 20. - Bs140. -   + Shipment      No. Catalogue: ADT200943


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