Submitted by Editor
Objective
To become familiar with the fact that geometry (similar triangles) can be used in real life to find height of certain things and width of many others. Description
In this project I tried to find situations in daily life where geometrical notions can be effectively used, I selected the following examples:
1. To find the width of a river
2. To find height of a tower
To find the width of a river
Fixed a pole at Q directly opposite to a tree P on the other side of the river. Walked along the river, fixed another pole at R at a distance of 9 metres. Walked another 3 metres to S, from here walked at right angles to the river till the point T is reached such that T is directly in line with R and P. Measured the distance ST. Using the property of similarity of triangles the width of the river was determined.
In right triangle RQP and RST
Angle PQR = angle RST = 90°
Angle PRQ = angle TRS (vertically opposite angles)
Therefore triangle RQP ~ triangle RST by AA corollary
QP_QR ST _ SR
_QP_9 ST _ 3
QP _ 3 ST " 1
Now ST = 4m, substituting its value in (i)
QP_ 3 4 _ 1
QP = 12m
Therefore width of river = 12m
To find the height of a tower
Placed the ruler upright in the shadow of the tower, so that the ends of its shadow is at the same place as the ends of the shadow of the tower. Knowing the relevant distance, the height of the tower can be estimated.
A 2m = 200 cm |
Solution :
In AABE and ACDE
angle E = angle E (common)
angle B = angle D = 90°
-AABE ~ ACDE
by AA corollary
AB = BE CD _ DE
(Corresponding parts of similar triangles)
200
..... (i)
CD 25
On measuring CD we get CD = 40cm
Substituting value of CD in (i)
,45 =200 > 40 25
200X40
:> AB =
25
= 320cm
= 3.2m
Height of tower = 3.2m
Conclusion
Thus we find that the geometry plays a very important role in our day to day life. Many examples involving different geometrical properties of triangles and circles could be examined. We can do lot of things which are impossible to measure for example:- Measuring height of tree, height of building etc.
In particular, in the given project we discover situations in which properties of similar triangles learnt in the classroom are useful.
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