Mathematics Lab Activity-14 Class X | Trigonometry

 Mathematics Lab Activity-14 Class X

Mathematics Laboratory Activities on Application of Trigonometry for class X students with complete observation tables strictly according to the CBSE syllabus.

Chapter - 09

Application of trigonometry

Activity - 14

Objective

To find the height of a building using a clinometer.

Material Required

Clinometer (a stand fitted with a square plate which is fitted with a movable 0º–360º protractor and a straw), a measuring tape 50 m long, table or stool.

Procedure

1. Place a table on the ground of a school.

2. Place a clinometer (a stand fitted with 0º–360º protractor and a straw whose central line coincides with 0º–360º line) on the table.

3. Now face it towards the building of the school.

4. Peep out through the straw to the top of the school building and note the angle (θ) through which the protractor turns from 0º–360º line..

Figure 1

5. Measure the height (h) of the centre of the protractor from the ground.

6. Measure the distance (d) of the building from the point lying on the vertical line of the stand (centre of the protractor) kept on table [see Fig. 1]. 

7. Repeat the above method keeping the clinometer at different positions and collect the values of q, h, d for different settings.

Observations & calculations

Using the knowledge of trigonometric ratios, we have :

θ is the angle measured through protractor.

where H is the height of the building.

h is the height of the protractor from the ground

d is the distance of building from the protractor.

i.e., H = h + dtanθ

S. no.	Angle Measured through Protractor (Angle of elevation)	Height of the protractor from the ground (h)	Distance (d) of the building from the centre of the protractor	tanθ	H = h + d tanθ
1	30o	50 m	100 m	Tan30o = 1/√3               = 0.58	H = 50 + 100 × 0.58     = 108 m
2	45o	50 m	58 m	Tan45o = 1.00	H = 50 +58 × 1     = 108 m
3	60o	50 m	33.5 m	Tan60o = √3              =1.73	H = 50 + 33.5 × 1.73     = 108 m
4	75o	50 m	15.5 m	Tan75o = 3.74	H = 50 + 15.5 × 3.74     = 108 m

Result

With the help of this activity we develop a formula to find the height of the building from any point away from the building. This formula is H = h + dtanθ. Height of the building remain same if we changes the distance of clinometer from the building.

Applications

1. A clinometer can be used in measuring an angle of elevation and an angle of depression.

2. It can be used in measuring the heights of distant (inaccessible) objects, where it is difficult to measure the height directly.

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