W3
Learning Area
Quarter
MATHEMATICS
4th
Grade Level
Date
9
I. LESSON TITLE
ANGLES OF ELEVATION AND ANGLES OF DEPRESSION
II. MOST ESSENTIAL LEARNING
Illustrates angles of elevation and angles of depression.
COMPETENCIES (MELCs)
M9GE-IVd-1
III. CONTENT/CORE CONTENT
IV. LEARNING PHASES AND LEARNING ACTIVITIES
I. Introduction (Time Frame: ____10 minutes____)
In this lesson, we will determine if the given angle is angle of elevation or angle of depression. This method is
commonly used by surveyors using special equipment to determine the exact measurement in measuring things that are
difficult to measure.
Definitions:
Line of sight is an imaginary line that connects the eye
of an observer to the object being observed.
The angle of elevation is the angle from the horizontal to
the line of sight of the observer to the object above.
The angle of depression is the angle from the horizontal
to the line of sight of the observer to the object below.
All pictures above are from MATHEMATICS GRADE 9
Learner’s Material, DepEd-BLR, First Editon, 2014, page 459
D. Development (Time Frame: ____30 minutes____)
Figure
Y
O
Horizontal
Line of
Sight
Line of
Sight
Angle of
Elevation
Angle of
Depression
⃗⃗⃗⃗⃗
𝑂𝐴
⃗⃗⃗⃗⃗
𝑂𝐵
none
∠𝐴𝑂𝐵
⃗⃗⃗⃗⃗
𝑂𝑌
⃗⃗⃗⃗⃗
𝑂𝑋
∠𝑌𝑂𝑋
none
IV. LEARNING PHASES AND LEARNING ACTIVITIES
⃗⃗⃗⃗⃗
𝑂𝐵
⃗⃗⃗⃗⃗
𝑂𝐴
∠𝐵𝑂𝐴
none
⃗⃗⃗⃗⃗
𝑂𝑋
⃗⃗⃗⃗⃗
𝑂𝑌
none
∠𝑋𝑂𝑌
⃗⃗⃗⃗⃗
𝑂𝑃
⃗⃗⃗⃗⃗
𝑂𝑅
none
∠𝑃𝑂𝑅
All pictures above are from MATHEMATICS GRADE 9 Learner’s Material, DepEd-BLR, First Editon, 2014, page 459
In identifying whether the given angle is an angle of elevation or an angle of depression:
1. Identify the horizontal line of sight. Usually, it is the horizontal line in the figure.
2. Identify whether the given object is above or below the horizontal line.
3. If the object is above the horizontal line, then use angle of elevation.
4. If the object is below the horizontal line, then use angle of depression.
IV. LEARNING PHASES AND LEARNING ACTIVITIES
E. Engagement (Time Frame: ___30 minutes______)
Complete the table below by identifying the needed information.
Figure
Horizontal
Line of Sight
Line of
Sight
Angle of
Elevation
Angle of
Depression
B
A
O
X
O
Y
Z
R
O
S
T
C
O
D
E
G
H
O
F
All pictures above are from MATHEMATICS GRADE 9 Learner’s Material, DepEd-BLR, First Editon, 2014, page 468
IV. LEARNING PHASES AND LEARNING ACTIVITIES
A. Assimilation (Time Frame: ____20 minutes_____)
Questions:
1. How did you identify the line of sight, angle of elevation and angle of depression?
2. What ideas have you learned from this activity?
3. Do you think you can use these ideas in your daily life?
4. Give and illustrate at least two situations in your life involving angle of elevation and angle of depression.
V. ASSESSMENT (Time Frame: ___30 minutes______)
(Learning Activity Sheets for Enrichment, Remediation, or Assessment to be given on Weeks 3 and 6)
Draw the pictures presented by the information in the problems given. Assume the buildings, ladders, etc. are all on level
ground.
1. The angle of elevation of the top of the building from a point 30 meters away from the building is 65°.
2. The angle of depression of a boy from a point on a lighthouse 30.5 meters above the surface of the water is 3°.
3. If an airplane that is cruising at an altitude of 9 km wants to land at NAIA, it must begin its descent so that the angle of
depression to the airport is 7°.
4. 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°.
5. Two points on the same side of a tree are 19.8 meters apart. The angles of elevation of the top of the tree are 21° from one
point and 16° from the other point.
VI. REFLECTION (Time Frame: _________)

Communicate your personal assessment as indicated in the Learner’s Assessment Card.

The learner, in their notebook, will write their personal insights about the lesson using the prompts below.
I understand that ___________________.
I realize that ________________________.
I need to learn more about __________.
Personal Assessment on Learner’s Level of Performance
Using the symbols below, choose one which best describes your experience in working on each given task. Draw it in the column
for Level of Performance (LP). Be guided by the descriptions below:
 - I was able to do/perform the task without any difficulty. The task helped me in understanding the target content/ lesson.
 - I was able to do/perform the task. It was quite challenging, but it still helped me in understanding the target content/lesson.
? – I was not able to do/perform the task. It was extremely difficult. I need additional enrichment activities to be able to do/perform this
task.
Learning Task
Number 1
Number 2
VII. REFERENCES
Prepared by:
LP
Learning Task
Number 3
Number 4
LP
Learning Task
Number 5
Number 6
LP
Learning Task
Number 7
Number 8
MATHEMATICS GRADE 9 Learner’s Material, DepEd-BLR, First Editon, 2014
Wilson Ray G. Anzures
Checked by:
MA. FILIPINA M. DRIO
LAILA R. MALOLES
HENRY P. CONTEMPLACION
GINALYN D. BELTRAN
LP