The this

Mathematics 9
Quarter 4
Self-Learning Module 8
Illustrating Angle of Elevation
and Angle of Depression
Mathematics – Grade 9
Quarter 4 – Self-Learning Module 8: Illustrating Angle of Elevation and Angle
of Depression
First Edition, 2020

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Published by the Department of Education – Schools Division of Pasig City

Development Team of the Self-Learning Module

Writers: Frank Luther Y. Gordon; Joan S. Magapi
Editor: Cherry O. Nabos; Revie G. Santos
Reviewers: Ma. Cynthia P. Badana; Ma. Victoria L. Peñalosa
Illustrator: Name
Layout Artist: Name
Management Team: Ma. Evalou Concepcion A. Agustin
OIC-Office of the Schools Division Superintendent
Carolina T. Rivera, CESE
OIC-Office of the Assistant Schools Division Superintendent
Manuel A. Laguerta EdD
Chief, Curriculum Implementation Division
Victor M. Javeña EdD
Chief, School Governance and Operations Division

Education Program Supervisors

Librada L. Agon EdD (EPP/TLE/TVL/TVE)

Liza A. Alvarez (Science/STEM/SSP)
Bernard R. Balitao (AP/HUMSS)
Joselito E. Calios (English/SPFL/GAS)
Norlyn D. Conde EdD (MAPEH/SPA/SPS/HOPE/A&D/Sports)
Wilma Q. Del Rosario (LRMS/ADM)
Ma. Teresita E. Herrera EdD (Filipino/GAS/Piling Larangan)
Perlita M. Ignacio PhD (EsP)
Dulce O. Santos PhD (Kindergarten/MTB-MLE)
Teresita P. Tagulao EdD (Mathematics/ABM)

Printed in the Philippines by Department of Education – Schools Division of

Pasig City
 Mathematics 9
Quarter 4
Self-Learning Module 8
Illustrating Angle of Elevation and
Angle of Depression
Introductory Message

For the Facilitator:

Welcome to the Mathematics Grade 9 Self-Learning Module on Illustrating

Angle of Elevation and Angle of Depression!

This Self-Learning Module was collaboratively designed, developed and

reviewed by educators from the Schools Division Office of Pasig City headed by its
Officer-in-Charge Schools Division Superintendent, Ma. Evalou Concepcion A.
Agustin, in partnership with the City Government of Pasig through its mayor,
Honorable Victor Ma. Regis N. Sotto. The writers utilized the standards set by the K
to 12 Curriculum using the Most Essential Learning Competencies (MELC) in
developing this instructional resource.

This learning material hopes to engage the learners in guided and independent
learning activities at their own pace and time. Further, this also aims to help learners
acquire the needed 21st century skills especially the 5 Cs, namely: Communication,
Collaboration, Creativity, Critical Thinking, and Character while taking into
consideration their needs and circumstances.

In addition to the material in the main text, you will also see this box in the
body of the self-learning module:

Notes to the Teacher

This contains helpful tips or strategies that
will help you in guiding the learners.

As a facilitator you are expected to orient the learners on how to use this self-
learning module. You also need to keep track of the learners' progress while allowing
them to manage their own learning. Moreover, you are expected to encourage and
assist the learners as they do the tasks included in the self-learning module.
 For the Learner:

Welcome to the Mathematics Grade 9 Self-Learning Module on Illustrating

Angle of Elevation and Angle of Depression!

This self-learning module was designed to provide you with fun and
meaningful opportunities for guided and independent learning at your own pace and
time. You will be enabled to process the contents of the learning material while being
an active learner.

This self-learning module has the following parts and corresponding icons:

Expectations - This points to the set of knowledge and skills

that you will learn after completing the module.

Pretest - This measures your prior knowledge about the lesson

at hand.

Recap - This part of the module provides a review of concepts

and skills that you already know about a previous lesson.

Lesson - This section discusses the topic in the module.

Activities - This is a set of activities that you need to perform.

Wrap-Up - This section summarizes the concepts and

application of the lesson.

Valuing - This part integrates a desirable moral value in the

lesson.

Posttest - This measures how much you have learned from the
entire module.
 EXPECTATIONS

1. Illustrate angle of elevation and angle of depression.

2. Differentiate angle of elevation and angle of depression.

PRETEST

Directions: Read each question carefully. Write the letter of your answer on a
sheet of paper.

1. What do you call the angle that is formed between a horizontal and a line of
sight above the horizontal line?
A. Vertical angle C. angle of elevation
B. Straight angle D. angle of depression

2. What do you call the angle that is formed between a horizontal and a line of
sight below the horizontal line?
A. Angle of depression C. angle of elevation
B. Acute angle D. reflex angle

3. What do you call an imaginary line that connects the eye of an observer to
the object?
A. Vertical line C. horizontal line
B. Line of sight D. diagonal line

4. If a man is standing on top of a mountain and looks downward, this represents

what kind of angle?
A. Vertical angle C. Angle of elevation
B. Angle of depression D. Negative angle

5. A group of students saw a rainbow in the sky after the rain in their window.
This represents:
A. Horizontal line C. Angle of elevation
B. Line of sight D. Angle of depression
 RECAP

Direction: Match Column A with the answers with Column B.

Column A Column B
a. −2 + √3
1. tan 45𝑜 − cos 45𝑜
2. cos 60𝑜 + sin 30𝑜 − tan 45𝑜 b.
2√3+3√2
3. tan 30𝑜 + cos 45𝑜 6

4. sin 60𝑜 + cos 30𝑜 2−√2

c.
5. 2 sin 60𝑜 − 2 tan 45𝑜 2

d. 0

e. √3
f. 1

LESSON

Let’s imagine that you are on top of a mountain looking down in an overlooking
city, how would you know the height of the mountain? If you flew a kite up in the
sky, what would be its height? In this self- learning module you will learn about
illustrating angles of elevation and depression and applying them in real-life
situations.
The angle of elevation is the angle between a horizontal line from the
observer and the line of sight to an object that is above the horizontal line.
In the diagram below, AB is the horizontal line. θ is the angle of elevation from the
observer at A to the object at C.

The angle of depression is the angle between a horizontal line from the observer and
the line of sight to an object that is below the horizontal line.

In the diagram below, PQ is the horizontal line. θ is the angle of depression from the
observer at P to the object at R.
 ACTIVITIES

ACTIVITY 1: LET’S PRACTICE!

Direction: Put a check (✓) on the box if the following scenarios represent angle of
elevation or angle of depression.

Angle of Angle of
Elevation Depression
1. A bird is seen by the observer flying up
in the sky and the angle formed is
55o10’.
2. A fisherman saw a school of fish
swimming just below his boat and the
angle formed is 67o11’.
3. The light from a light house can be
seen in the open sea as seen by the
observers who went sailing their ships
at night and the angle formed is
48o15’.
4. A kite is seen flying up in the sky by
an observer and makes an angle
measure of 77o25’.
5. A tourist went on top of a mountain to
see the scenery at the foot of the
mountain and the angle formed is
61o23’.

ACTIVITY 2: KEEP PRACTICING!

Direction: Write Angle of Elevation or Angle of Depression on the space provided
before each number.
________________ 1. An observer is standing on a rooftop, and he saw a kite in the
sky.
________________ 2. A diver saw a school of sardines swimming above him.
________________ 3. A pilot saw an island below him.
________________ 4. At night, when you look at the window and glance at the sky, you
will see lots of stars and some of the planets.
________________ 5. When you go at the building’s rooftop you can see people at the
ground below you.
ACTIVITY 3: TEST YOURSELF!
Direction: Put a check (✓) on the box if the following pictures represent Angle of
elevation or Angle of Depression.

Angle of Angle of
elevation depression
1.

2.

3.

4.

5.

WRAP-UP

Angle of elevation - is the angle between a horizontal line from the observer
and the line of sight to an object that is above the horizontal line.

Angle of depression - is the angle between a horizontal line from the observer
and the line of sight to an object that is below the horizontal line.
 VALUING

REFLECTION: (Journal Writing)

“The one who falls and gets up is stronger than the one who never tried. Do
not fear failure but rather fear not trying.”― Roy T. Bennett, The Light in the Heart
In your opinion, what are your experiences that you’ve been down but still you
tried to get up to make things right?

POSTTEST

Directions: Read each of the following carefully. Choose the letter that corresponds
to the correct answer.

1. What do you call the imaginary line that connects the eye of an observer to
the object being observed?
A. Line of sight C. Vertical line
B. Diagonal line D. Horizontal line

2. What do you call the angle that is formed from the horizontal to the line of
sight of the observer to the object above?
A. Line of sight C. Angle of depression
B. Angle of elevation D. Horizontal

3. What do you call the angle that is formed from the horizontal to the line of
sight of the observer to the object below?
A. Horizontal C. Line of sight
B. Vertical D. Angle of depression

4. The angle to the top of the building from a point 30 meters away from the
building that makes an angle of 65o11’ is an example of _____________.
A. Angle of depression C. Horizontal
B. Angle of elevation D. Vertical

5. 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 the airplane to the airport is 7o18’
is an example of _____________.
A. Vertical line C. Angle of elevation
B. Angle of depression D. Horizontal line
 KEY TO CORRECTION
5. B 4. B 3. D 2. B 1. A
POSTTEST
✓ 5
✓ 4
✓ 3
✓ 2
✓ 1
Angle of elevation Angle of depression
ACTIVITY 3: TEST YOURSELF
3. Angle of depression
2. Angle of elevation 5. Angle of depression
1. Angle of elevation 4. Angle of elevation
ACTIVITY 2: KEEP PRACTICING
✓ 5
✓ 4
✓ 3
✓ 2
✓ 1
Angle of depression Angle of elevation
ACTIVITY 1: LET’S PRACTICE
5. a 4. e 3. b 2. d 1. c
RECAP
5. C 4. B 3. B 2. A 1. C
PRETEST

References
Angles of elevation and depression
https://www.onlinemathlearning.com/angle-of-elevation.html
(accessed July 9, 2020)
Angle of Elevation stock images
https://www.123rf.com/stock-photo/angle_of_elevation.html
(accessed, July 9, 2020)
Bryant, Merden, Leonides Bulalayao, Melvin Callanta, Jerry Cruz,
Richard De Vera, Gilda Garcia, Sonia Javier, Roselle Lazaro, Bernadeth
Mesterio, Hero Saladino. MATHEMATICS Learner’s Material 9, Vibal
Group Inc. 2014
Oronce, Orlando and Marilyn Mendoza. E-MATH 9, Manila: Rex Bookstore,
Inc., 2015