FORMATIVE ASSESSMENT
Project work:Preliminary Information:
Class: 10th
Subject: Mathematics
Name of the unit: Application of Trigonometry
No. of the projects:
Medium: English
Allotment of work: Group Work
1) Collect the information
2) Record the data
3) Analyse the data
4) Present project.
Detailed information of the project:
Title of the project: Find the height of a building / tree by using clinometer
Objectives of the project: To find the height of a building/ tree (without climbing it) using trigonometry
Material used: clinometer, graph, paper, pencil, rubber etc.
Tools: Identify the building/ tree for finding height.
Procedure:
Observe the following figure it is known as clinometer.
Collection of Data:
Select the object. Let it be a tree. Observe the tree 'AB' from a distance of 30 m from the foot of the tree. Let the observing point C. From the observing point C, with the help of clinometer tube (on horizontal line there is a hallow tube) see the top of the tree.
Note: The angle shown by the indicator. Let it be 30°.
Then by using trigonometric ratios, we can calculate the height of the tree.
Analysis:
Height of the tree = AB
Distance between foot of the tree B and
Observing point C is BC = 30 m
Angle of elevation at C is 30°
... AB = 10 (1.732)
= 17.32 m
... Height of the tree is AB = 17.32 m.
Conclusion:
From this project we conclude that we can measure the height of any building / tree / pole by using clinometer.
Experiences of the students:
i) We enjoyed while doing this project.
ii) We learnt how to make clinometer to measure the heights and distances.
Doubts and Questions:
Is the measurements are accurate or not?
Acknowledgments:
We convey our sincere thanks to our guide teacher
Reference books/resources:
i) APSCERT, X − Maths Textbook
ii) NCERT, X − Maths Textbook
iii) Mathematics projects by N.M. Rao
Signatures of the students:
FORMATIVE ASSESSMENT
Test on Applications of Trigonometry
CLASS: X TIME: 45 Min.
I. Answer the following questions. 3 × 2 = 6
1. The top of a clock tower is observed at an angle of α° and the foot of the tower is at the distance of 'd' meters from the observer. Draw the diagram for this data?
2. A boy observed the top of an electric pole at an angle of elevation of 60° when the observation point is 8 m away from the foot of the tower. Find the height of the pole?
3. An observer of height 1.8 m is 13.2 m away from a palm tree. The angle of elevation of the top of the tree from his eyes is 45°. What is the height of the palm tree?
II. Answer the following questions. 2 × 1 = 2
4. Aperson is flying a kite at an angle of elevation α° and the length of thread from his hand to kite is 'I'. Draw a diagram for the situation.
5. Define angle of elevation?
III. Answer the following questions. 2 × 4 = 8
6. Two men on either side of a temple of 30 m height observe its top at the angles of elevation 30° and 60° respectively. Find the distance between the two men?
7. From the top of a building, the angle of elevation of the top of a cell tower is 60° and the angle of depression to its foot is 45°. If distance of the building from the tower is 7 m. Then find the height of the tower.
IV. Choose the correct option and put the capital letter in the given bracket. 8 × 
= 4
8. The length of the shadow of a man is equal to the height of man. The angle of elevation is ( )
A) 90° B) 60° C) 45° D) 30°
9. The length of the shadow of a pole 30 m hight at some instant is 10
m. The angle of elevation of the sun is ( )
A) 90° B) 60° C) 45° D) 30°
10. Find the angle of depression of a boat from the bridge at a horizontal distance of 25 m from the bridge ( )
A) 45° B) 60° C) 30° D) 15°
11. The tops of two poles of height 10 m and 18 m are connected with wire . If wire makes an angle of 30° with horizontal, then length of wire is ( )
A) 10 m B) 18 m C) 12 m D) 16 m
12. From a point 20 m away from the foot of the tower, the angle of elevation of the top of the tower is 30°. The height of the tower is ...... m. ( )
13. The ratio of the length of a tree and its shadow is 1 : 
the angle of elevation of the sun is ( )
A) 30° B) 45° C) 60° D) 90°
14. The angle of elevation of the sun is 45°. The length of the shadow of a 12 m hight tree is ( )
A) 24 m B) 6 m C) 12 m D) None
15. If two towers of height h1 m and h2 m subtend angles of 60° and 30° respectively at the midpoint of the line joining their feet, then h1 : h2 is ( )
A) 1 : B) : 1 C) 1 : 
D) : 1
Writer: T.S.V.S. Suryanarayana Murthy
