The document is a classroom observation for a Grade 9 mathematics lesson on trigonometry, specifically focused on angles of elevation and depression. It includes activities for students to identify objects at various eye levels, practical problems involving angles, and illustrations related to real-life applications of these concepts. Additionally, the document contains a series of exercises and questions to reinforce learning and practical application of trigonometric principles.

1. Classroom Observation No. 4
Grade 9 Mathematics
Querubee D. Diolula
TRIGONOMETRY

2. As you go through this lesson, think of these important questions:
 “How to describe angle of elevation and angle
of depression?
 “How to illustrate and solve angle of elevation
and angle of depression?
 “What is the importance of angle of elevation
and depression in our daily life?

3. 4 Pics 1 Word
__ L __ __ A __ __ __ N

4. 4 Pics 1 Word
E L E V A T I O N

5. 4 Pics 1 Word
__ E __ __ E __ S __ __ N

6. 4 Pics 1 Word
D E P R E S S I ON

7. LOOK UP
LOOK DOWN

8. Follow the steps below and answer the questions that follow:
1. Move around the room. Find one object that is at your eye level
and list them on the table and make an illustration of:
A. Objects at Eye Level
2. Let’s go outside. Find one object/structure that is above your eye
level and list them on the table and make an illustration of:
B. Objects above Eye Level
3. Now, find one object/structure that are below your eye level and
list them on the table and make an illustration of.
C. Objects below Eye Level

9. LOOK UP LOOK DOWN
1.How did you find the activity?
2.Describe the illustrations you have
created from the activity.
3.What mathematical concepts have you
learned from the activity?
4.When you look up at the things above
your eye level, is there an angle formed?
5.How about when you look down?
6.Do you think you can directly measure
the height of the object/structure you
have listed in the activity?

10. Angle of Elevation
Angle of Depression

11. LINE of SIGHT
It is an imaginary
line that connects
the eye of an
observer to the
object being

12. LINE of SIGHT

13. ANGLE of ELEVATION
It is the angle from
the horizontal to the
line of sight of the
observer to the
object ABOVE.

14. ANGLE of DEPRESSION
It is the angle from
the horizontal to the
line of sight of the
observer to the
object BELOW.

15. Identify Me!

16. Complete the table below by identifying the needed information.
Horizontal
Line of Sight
Line of
Sight
Angle of
Elevation
Angle of
Depression

17. Complete the table below by identifying the needed information.
Horizontal
Line of Sight
Line of
Sight
Angle of
Elevation
Angle of
Depression
𝐴𝐵 𝐴𝐶 NONE ∠𝐵𝐴𝐶

18. Complete the table below by identifying the needed information.
Horizontal
Line of Sight
Line of
Sight
Angle of
Elevation
Angle of
Depression

19. Complete the table below by identifying the needed information.
Horizontal
Line of Sight
Line of
Sight
Angle of
Elevation
Angle of
Depression
𝐶𝑂 𝐶𝐷 ∠𝐷𝐶𝑂 NONE

20. 𝐴𝐵 𝐴𝐶 NONE
∠𝐵𝐴𝐶
𝐶𝑂 𝐶𝐷 ∠𝐷𝐶𝑂 NONE
How did you identify the line of sight, angle of
elevation and angle of depression?

21. 𝐴𝐵 𝐴𝐶 NONE
∠𝐵𝐴𝐶
𝐶𝑂 𝐶𝐷 ∠𝐷𝐶𝑂 NONE
What ideas have you learned from this
activity?

22. 𝐴𝐵 𝐴𝐶 NONE
∠𝐵𝐴𝐶
𝐶𝑂 𝐶𝐷 ∠𝐷𝐶𝑂 NONE
Do you think you can use these ideas in
your daily life?

23. 𝐴𝐵 𝐴𝐶 NONE
∠𝐵𝐴𝐶
𝐶𝑂 𝐶𝐷 ∠𝐷𝐶𝑂 NONE
Give and illustrate at least two situations in
your life involving angle of elevation and angle
of depression

24. Draw the pictures presented by the information in
the problems given.
1.The angle of elevation of the top of the
building from a point 30 meters away
from the building is 65°. What is the
height of the building?
2. An airplane is flying at a height of 4
kilometers above the ground. The
distance along the ground from the
airplane to the airport is 6 kilometers.
What is the angle of depression from the
airplane to the airport?
Examples:

25. What is the importance of angle
of elevation and depression in
our daily life?

26. Multiple Choice. Write the correct answer before each number.
__1. The line that connects the eye of an observer to the object is
called _____.
A. horizontal line B. straight line C. line of sight D. vertical line
__2. The baby is looking at the moon. The angle formed from the baby to
the moon is an_____.
A. angle of
depreciation
B. angle of
elevation
C. angle of
depression
D. angle of
oppression
__3. The angle from the horizontal to the line of sight of the observer to the
object below is called ________.
A. angle of
elevation
B. right angle C. angle of
depression
D. acute
angle
__4. On the figure above, what is the angle of depression?
A. Angle 1 B. Angle 2 C. Angle RPT D. Angle TPR
__5. On the figure above, what is the line of sight from the pilot of the
aircraft going to the tower?

27. Draw the pictures presented by the information in
the problems given.
RUBRIC
CRITERIA Highest Possible Score
Structure 10 points
Cleanliness 5 points
Timeliness 5 points
Total 20 points

28. Draw the pictures presented by the information in
the problems given.
1.A hiker is 400 meters away from
the base of a radio tower. The
angle of elevation to the top of the
tower is 46°.
2.A bird sits on top of a 5-meter lamp
post. The angle of depression from
the bird to the feet of an observer
standing away from the lamp post
is 35°.

29. THANK YOU
GODBLESS

30. ANGLES OF
ELEVATION
AND
DEPRESSIO
N

31. Draw the pictures presented by the information in
the problems given.
1.A hiker is 400 meters away from
the base of a radio tower. The
angle of elevation to the top of the
tower is 46°.
2.A bird sits on top of a 5-meter lamp
post. The angle of depression from
the bird to the feet of an observer
standing away from the lamp post
is 35°.

32. Solve the following angle of elevation and
depression using the figures.

33. Solve the following angle of elevation and
depression using the figures.

34. Solve the following angle of elevation and
depression using the figures.

35. Solve the following angle of elevation and
depression using the figures.

36. Illustrate and solve the given problems.
If a guy wire for a tree is
8 𝑚 long, making 40°
angle with the ground,
how far is base of the
tree from the state
anchoring the wire?

37. Illustrate and solve the given problems.

38. Illustrate and solve the given problems.
The angle of elevation to
the top of a city plaza’s
fountain from a point
12 𝑚 from itss base is
32°, find the height of
the fountain.

39. Illustrate and solve the given problems.

40. Illustrate and solve the given problems.
An end of a ladder is
leaning against a wall. The
other end forms a 53° with
the floor. If the ladder
measures 16 ft., how far is
one end of the ladder from
the wall?

41. Illustrate and solve the given problems.

42. Illustrate and solve the given problems.
Using the previous
illustration, solve for the
height of the wall from the
floor up to the point where
the ladder is leaning.

43. Illustrate and solve the given problems.
A bird is looking at a worm on
the ground. If the shortest
diagonal distance between the
bird and worm is 25 meters
and the horizontal distance is
18 meters, solve for the angle
of depression.

44. Illustrate and solve the given problems.

45. Illustrate and solve the given problems.
A CCTV camera is mounted on a
wall 3 𝑚 above a bank teller’s
desk. It is used to view the bank’s
entrance door which has a
horizontal distance of 10 𝑚 from
the camera. Find the angle of
depression from the camera lens
to the entrance door.

46. Illustrate and solve the given problems.

47. Illustrate and solve the given problems.
From a height 42 𝑚 above
sea level, two ships are
sighted due east. The
angles of depressions are
52° and 27°. How far apart
are the ships?

48. Illustrate and solve the given problems.