To Study

Geometry in Real Life

To become familiar with the fact that geometry (similar triangles) can be Description

In this project I tried to find situations in daily life where geometrical notions can be effectively used, I selected the following examples: 2. To find height of a tower 1. To find the width of a river

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used in real life to find height of certain things and width of many others.

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Objective

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To find the width of a 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. width of the river was determined. Measured the distance ST. Using the property of similarity of triangles the

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Fixed a pole at Q directly opposite to a tree P on the other side of the river.

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In right triangle RQP and RST Angle PRQ = angle TRS (vertically opposite angles)   ൌ    ͻ ൌ  ͵
୕୔ ୗ୘

Therefore triangle RQP ~ triangle RST by AA corollary

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ଷ ଵ

------- (i)

Now ST = 4m, substituting its value in (i)  ͵ ൌ Ͷ ͳ

Therefore width of river = 12m

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QP = 12m

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Angle PQR = angle RST = 90°

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To find the height of a tower 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.

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Placed the ruler upright in the shadow of the tower, so that the ends of its

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Solution :
In ∆ABE and ∆CDE angle E = angle E (common) angle B = angle D = 90°

by AA corollary
୅୆ େୈ

=

ୈ୉ ଶ଴଴ ଶହ

୆୉

஺஻ ஼஽

=

………

(i)

On measuring CD we get CD = 40cm Substituting value of CD in (i)
‫ܤܣ‬ ൌ൐  ͶͲ ଶ଴଴ ଶହ

=

= 320cm = 3.2m

‫׵‬Height of tower = 3.2m

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ൌ൐ AB =

ଶ଴଴ൈସ଴ ଶହ

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(Corresponding parts