Geometry in Real Life
Description In this project we try to find situations in daily life where geometrical notions can be effectively used - Geometry in Real Life introduction. In particular, in the following examples the student discovers situations in which properties of similar triangles learnt in the classroom are useful. Students need to be made aware of the fact that the study of geometry arose in response to certain human needs. They should know about the use of geometry in our daily or real life. In this project, students will discover situations in daily life where geometrical concepts can be used effectively.
In particular we find situations where the properties of similar triangles are useful and how to find height and distance of any object with the help of geometry and trigonometry. Objective 1) To find breadth of a canal/river 2) To find the height of tree/tower Pre-requisite knowledge 1) Properties of similar triangles 2) Knowledge of trigonometry 3) Knowledge of finding height and distance Methodology 1) to find breadth of a canal/river a) Fix a pole at point B on the bank of the river directly opposite to a tree A on the other bank, as shown in fig.
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1. 1. b) Walk a known distance along the bank and fix another pole at C. Walk another known distance to a point D. From D, walk at right angle to the bank till the point P is reached such that P is directly in line with C and A i. e. P ,C & A are in a straight line , as shown in fig. P 1-1. c) Measure the distance PD. RESULT 1) Let BC = a unit, DC= b unit and PD= c (These are all known distances) 2) Let the breadth of the river be d unit 3) Note that angle s ABC and PDC are similar, 4) Hence, AB/PD=BC/DC: – d/c = a/b: – d =ac/b.
5) Hence the breadth of the river =ac/b units 2) To find the height of a tower/ tree A). Fix a ruler(in the vertical position) of known height in the shadow of the tree such that the end point of the shadow of the ruler is at the same point as the end of the shadow of the tree , as shown in fig. P- 2b. b) Measure BE and DE. RESULT Let BE=a units, DE= b units and height of ruler = c units. Let the height of the tree be h units. Note that angle ABE and CDE are similar Hence AB/CD = BE=DE: – h/c =a/b: – h =ac/b Hence the height of the tower =ac/b units
[pic] LEARNING OUTCOME 1) Student knows the role of geometry in daily life 2) Student appreciates the role of geometry in daily life. 3) As part of this project students should think of examples involving different geometrical properties of triangles and circles. [pic] FIGURE 1. 1 ACKNOWLEDGEMENT I would like to thank my honorable guide …………. for her regular guidance, constant supervision and readiness to supply required facts on the project and inspiring encouragement given to me time to time in completion of my project.
Her untiring help, sincere criticism, meticulous attention and sympathetic attitude have left no stone unturned in conveying the present work. May I take this opportunity in expressing my sincere thankfulness to all those who helped me in one way or the other towards the project. TABLE OF CONTENTS |S. NO. | | |1
|Acknowledgement | |2 |Introduction | |3 | | |4 | | |5 | | |6 | | |7 | | |8 | | |9 | | |10 | | |11 | | |12 | | |13 | | |14 | | |15 | | |16 | | |17 | | |18 | | |19 | | |20 | | |21 | | 56