This document contains a detailed lesson plan for teaching Grade 9 students about angles of elevation and depression. The plan includes objectives, materials, procedures, examples, and an evaluation. Students will learn to describe, illustrate, and solve problems involving angles of elevation and depression. The lesson proper involves defining key terms, working through example problems step-by-step, and having students complete practice problems in groups. The evaluation assesses students' understanding through multiple choice and illustration questions.

1. A DETAILED LESSON PLAN IN MATHEMATICS FOR GRADE NINE
Aimee M. Cadeliña
April 20, 2017
I. OBJECTIVE
At the end of a 60-minute period, the Grade Nine students will be able to describe, illustrate
and solve problems involving angle of elevation and angle of depression with 75%
proficiency level.
II. SUBJECT MATTER
ANGLE OF ELEVATION AND ANGLE OF DEPRESSION
A. Reference
Algebra Two with Trigonometry by Foster, Ruth, and Winters
B. Materials
Visual aid, board, chalk and calculator
C. Ideas
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.
D. Processes
Describing, illustrating, solving
E. Values
Active participation, cooperation, collaboration and thinking
III. PROCEDURE
A. Preliminary Activities
1. Prayer
2. Checking of the attendance
3. Checking of the assignment
4. Review of the past lesson
5. Drill/Exercise
B. Motivation
Group Activity on Angles of Elevation and Depression
C. Lesson Proper
TEACHER ACTIVITY STUDENT ACTIVITY
Our topic for today is about angle of elevation
and angle of depression.
Do you have any idea class of what do we mean
by elevation?
How about depression?
Angle of elevation is the angle form the
horizontal to the line of sight of the observer to
the object above.
Line of sight is an imaginary line that connects
the eye of an observer to the object being
observed.
The answer of the students may
vary.

2. Angle of depression is the angle from the
horizontal to the line of sight of the observer to
the object below
To understand better, let us consider an
example.
Problem No.1
An observer looks up at an angle of 40° looking
at the top of a tower. The tower is 300ft away
measured along the ground. What is the height
of the tower?
Now what you are going to do is to draw first a
right triangle then base on the problem, label the
right triangle similar to the previous problem
you have encountered before.
Suppose that this is the Tower and this is the
observer. In the Problem the observer looks up
the angle of 40° looking at the top of a Tower.
Is the angle of 40°, an angle of elevation or an
angle of depression?
Very good! So where do we put the 40° angle?
Is it between the observer’s line of sight and the
top of a tower, or between the observer’s line
sight and line of sight above observer?
Very Good! So we are asked to find the height
of the tower right? So let h be the height of the
tower.
What trigonometric functions or ratio can be
used to solve for the height of the tower?
Okay let’s try to solve the height of the tower
using tangent function.
𝑇𝑎𝑛𝑔𝑒𝑛𝑡 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝑇𝑎𝑛 40˚ =
ℎ
300𝑓𝑡
(𝑇𝑎𝑛 40˚)(300) = ℎ
251.73 𝑓𝑡 = ℎ
The height of the tower is 251.73𝑓𝑡
Are there any questions?
The student will follow.
Angle of elevation Ma’am!
Between the observer’s line of sight
and the line of sight above observer
Ma’am!
Tangent Function
None Ma’am!

3. Problem no.2
An airplane is flying at a height of 4 km
above the ground. The distance along the
ground from the airplane to the airport is 6
km. What is the angle of depression from
the airplane to the airport?
Our notation for degrees is θ
If this is our illustration, the height of the
airplane to the ground is 4 km and the
distance along the ground is 6 km then
where should we put the angle of depression
or the θ?
Suppose the observer is in the inside on the
airplane. Then our line of sight must be the
eye level of the observer, right?
So where should we put the angle of
depression or the θ?
Between the observer line of sight and
airport, between the horizontal ground and
airplane or between the observer line sight
and line of sight below observer?
Very Good!
So by definition of angle of depression it is
between the observer line sight and line of
sight below observer.
Okay to solve θ, what trigonometric ratios
can be used to solve the angle of
depression?
Okay! Tangent! So Tangent is opposite over
adjacent.
So who wants to volunteer to solve for θ
using tangent function? Anyone? Yes!
Do you have the same answer class?
Yes Ma’am!
between the observer line sight
and line of sight below observer
Tangent Ma’am!
Yes Ma’am!
The student will raise his her
hands
𝑇𝑎𝑛 𝜃 =
4
6
tan θ= 0.67
tan θ= 𝑡𝑎𝑛(0.67)−1
θ=33.82°
Yes Ma’am!

4. Who has another answer?
Are there any questions?
None Ma’am!
None Ma’am!
D. Generalization
What is an angle of elevation?
What is an angle of depression?
E. Application
Right now, let’s have an activity. Please count off from1-4 starting from you. Group 1
please stand up know your group mates and occupy in that area, similar with 2 on that
area, 3 on that area and 4 on that area.
Answer the following questions in a
1
2
sheet of paper.
1. In the diagram below, AB and CD are two vertical poles on horizontal ground. Draw
in the angle of elevation of D from B and the angle of depression of C from B.
2. An observer looks up at an angle of 40˚ looking at the top of a tower. The tower is
200 ft. away from the observer. What is the height of the tower?
IV. EVALUATION
Choose the right answer.
1. ___________ is an angle from the horizontal to the line of sight of the observer to the
object below.
A. Angle of Bowling C. Angle of Depression
B. Angle of Candid D. Angle of Elevation
2. What do you call an angle from the horizontal to the line of sight of the observer to the
object above?
A. Angle of Bowling C. Angle of Depression
B. Angle of Bowling D. Angle of Elevation
3. What do you call an imaginary line that connects the eye of an observer to the object
being observed?
A. Greenwich Line C. Mediterranean Line
B. Line of Sight D. Polar Line
4. This angle is formed when you’re looking for a lost coin in the end.
A. Angle of Bowling C. Angle of Depression
B. Angle of Candid D. Angle of Elevation
5. This angle is formed when you’re looking at the top of the tree a hundred feet away from
you.
A. Angle of Bowling C. Angle of Depression
B. Angle of Candid D. Angle of Elevation

5. V. ASSIGNMENT
Illustrate and solve the following questions.
1. Two poles on horizontal ground are 60 m apart. The shorter pole is 3 m high. The angle
of depression of the top of the shorter pole from the top of the longer pole is 20˚. Sketch a
diagram to represent the situation.
2. A kite held by 100 m of string makes an angle elevation with the ground of about 50°,
how high is the kite above the ground?
3. From the top of a vertical cliff 50 m high, the angle of depression of an object that is level
with the base of the cliff is 65º. How far is the object from the base of the cliff?