Mathematics Project on Geometry in Real Life
Mathematics Project on Geometry in Real Life
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:
- To find the width of a river
- To find the 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 ... (i)
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 distances, the height of the tower can be estimated.
Solution:
In triangles ABE and CDE:
- Angle E = Angle E (common)
- Angle B = Angle D = 90°
Therefore triangle ABE ~ triangle CDE by AA corollary:
AB / BE = CD / DE (Corresponding parts of similar triangles)
AB / 200 = CD / 25 ... (i)
On measuring CD we get CD = 40cm. Substituting value of CD in (i):
AB / 200 = 40 / 25
AB = (200 × 40) / 25
AB = 320cm
AB = 3.2m
Height of tower = 3.2m
Conclusion
Thus we find that 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 many things which are otherwise impossible to measure directly, for example measuring the height of a tree or the height of a building.
In particular, in this project we discover situations in which properties of similar triangles learnt in the classroom are useful.