10th maths model project in trigonometry

X CLASS  MATHS MODEL PROJECT TRIGONOMETRY

I Preliminaries:

Names o f the students :

 I)

2)

3)

4)

5)

Title of the project: Finding Heights – Distances

Objectives: To find the height of a tree without climbing it

 Hypothesis: Height of the tree    mtrs.

 Required material:

A hallow cylindrical long pipe, a plastic card board, sheet cut in semi circle, thread and a weight.

Figure:

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Method:

This project is carried out based on practical / experimental method

Step-I (Construction of Instruments)

Tak a cylindrical tube AB. Fig. 1 fix the semicircle shaped card board as shown. Fix one end of the thread at the midpoint ‘O’ and weight to the other end of the thread. Angles are marked on the semicircular card board from 0° -90° on both sides as shown in the figure. Now, with this apparatus we can find the angle of elevation.

Step-II (Using the apparatus - and finding the angle of elevation practically)

First the distant object T is focused (i.e.: the top of the tree is focused) through the focus pipe. The thread shows an angle when we focus on the protractor. The values of this angle of elevation must be noted in a given proforma. Repeat this 2 or 3 times.

Table-1:

Showing the value of  angles   Of  elevation, perpendicular distance

SI. No.	Angle of elevation (0)	Perpendicular distance between observer and tree (m)
1 2 3

Data Analysis:

By using the angle (θ), and distance (m) we can find the height of the tree, using trigonometric ratios as follows:

Tan θ = PT/AT         =HEIGHT OF THE TREE / PERPINDICULAR DISTANCE

Height of the tree = Distance X Tan θ.

(we will find the height of the tree, by substituting the 0 value from tangent values).

Table-2:

SI. No.	Angle (0)	Tan (0) =	Perpendicular distance (d) m	Height of the tree = (d X Tan 0)
1 2 3

Observation : By observing the above values, the height of the tree=      

Result : H eight of the (target) tree =    m.

Conclusion :

Thus, we can find the heights and distances by the help of such an apparatus called clinometers and using the trigonometric principles.

If we knowthe height we can find the distance between target and observation point and viceverse.

This method very useful in finding the width of rivers etc. And these applications are useful in Civil engineering, etc.

References :

<![if !supportLists]>1)                 <![endif]>Maths cas kit, NCERT

<![if !supportLists]>2)                 <![endif]>10th class text book NCERT

<![if !supportLists]>3)                 <![endif]>Methods of Teaching mathematics - Telugu Academy