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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.

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 Geometry in Real Life 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 ൌ ൌ ͻ ͵ ୕ ୗ ൌ ଷ ଵ ------- (i) Now ST = 4m, substituting its value in (i) Ͷ ൌ ͵ ͳ 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. Solution : In ∆ABE and ∆CDE angle E = angle E (common) angle B = angle D = 90° ∆ABE ~ ∆CDE by AA corollary େୈ = ୈ (Corresponding parts of similar triangles) = ଶ ଶହ ……… (i) On measuring CD we get CD = 40cm Substituting value of CD in (i) ൌ ܣܤ ͶͲ =ଶ ଶହ ൌ AB = ଶൈସ ଶହ = 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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