Geometry in Real Life
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Description
In this project we try to find situations in daily life where geometrical notions can be effectively used. 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.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
Description
In this project we try to find situations in daily life where geometrical notions can be effectively used. 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.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