CENTRAL BICOL STATE UNIVERSITY OF AGRICULTURE San Jose, Pili, Camarines Sur COLLEGE OF DEVELOPMENT EDUCATION – LABORATORY HIGH SCHOOL FINAL DEMONSTRATION DETAILED LESSON PLAN IN MATHEMATICS IV February 29, 2012, 1:00 – 2:00 p.m IV – A I. OBJECTIVES
At the end of the lesson, the students are expected to: 1. use the appropriate trigonometric function in solving problems involving angles of elevation and angles of depression. 3. relate the terms elevation and depression in real life. II. SUBJECT MATTER
A. Topic: Applications of Trigonometric Functions B. Sub-topic: Solving Problems involving Angles of Elevation and Angles of Depression C. References: e-Math (Advanced ( Advanced Algebra and Trigonometry) Trigonometry) IV by Orlando A. Oronce and Marilyn Ma rilyn O. Mendoza, pages 298 – 301. Advanced Algebra by Soledad Jose-Dilao, Ed.D. page 218. http://www.search-document.com/ppt http://www.search-document.com/ppt/1/2/angle=of=el /1/2/angle=of=elevation.html# evation.html# http://www.slidemath.com/rpoly http://www.slidemath.com/rpoly/Trigapps.shtm /Trigapps.shtmll http://www.syvum.com/cgi/on http://www.syvum.com/cgi/online/fillin.cgi/m line/fillin.cgi/math/trigo/trig3 ath/trigo/trig3.tdf?0 .tdf?0 http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-888484-5&chapter=8&lesson=5&&headerFile=7
D. Materials: computers, projector, white board Instructional Materials: cut-out pictures/images pictures/images of objects to be used in the group activity, slide and video presentations, online scientific calculator, online Right Triangle Solver, foldable E. Skills to be developed: problem solving skills, relating, computational skills and analytical thinking skills F. Values to be integrated: patience, accurateness, teamwork/cooperation, teamwork/cooperation, being humble & being a positive thinker G. Subject to be integrated: ICT H. Concepts: 1. The angle of elevation is the angle between the imaginary line of sight and horizontal line, where the object is above the observer. 2. The angle of depression is the angle between the imaginary line of sight and a horizontal line, where the object is below the observer. 3. Solving right triangles means finding the lengths of the sides and measures of the acute angles of the triangle. I. Methodology: 4 A’s of Learning (Activity, Analysis, Abstraction, and Application) III. LEARNING ACTIVITIES TIME FRAME
7mins
TEACHING HINT
A. Preliminary Activities 1. Greetings
TEACHER’S ACTIVITY
Good afternoon class!
STUDENT’S ACTIVITY
Good afternoon Sir!
2. Opening Prayer
May I ask everyone to please (The students will follow) stand for the opening prayer. (Mathematical prayer downloaded from YouTube will be played)
3. Securing cleanliness and orderliness
Before you take your seats, please make sure that there are no pieces of dirt on the floor. Also, arrange the chairs properly.
4. Checking of Attendance
Class beadle, who are absent today?
None Sir!
5. Checking of Assignment
Please submit your assignment.
(The students will submit their assignment)
(The students will follow)
IM’s
6. Recall
Before we start our lesson, let us first sing the SOH-CAH-TOA song as memory aid in Solving Right Triangle.
(The students will sing the SOHCAH-TOA Song)
Did you like the song?
Yes Sir!
down loaded youtube video
Let us recall again the sine, cosine and tangent ratio.
Sine θ is the ratio of what side?
sin θ =
What about cos θ?
cos θ =
How about tan θ?
tan θ =
slide presenta tion
Very Good! 4 mins
B. Motivation
To start the new lesson, let us take a look these illustrations. (Show animated pictures regarding angles of elevation and depression)
slide presenta tion
Illustration A line of sight
horizontal line
Illustration B horizontal line
line of sight
In illustration A, what can you say about the line of sight from Budoy to the airplane with respect to the horizontal line?
The line of sight from Budoy to the airplane is above the horizontal line.
What about in illustration B? What can you say about the line of sight from Budoy to Jackie with respect to the horizontal line?
The line of sight from Budoy to Jackie is below the horizontal line.
What geometric figure is formed by the line of sight and the horizontal line in the two illustrations?
The geometric figure that was formed by the line of sight and the horizontal line in the two illustrations is an angle.
Bright observations! 1 min
C. Presentation of the lesson
That angle in Illustration A and B is what we call angle of elevation and angle of depression
slide presenta tion
respectively. And we shall learn more about these concepts as we go on with our lesson today which is about Solving Problems involving Angles of elevation and Angles of depression. 1 min
D. Presentation of the Objectives
For today’s lesson, here are the objectives. (Objectives will be flashed on the screen) Who can read the objectives?
5 mins
E. Unlocking of Difficulties
slide presenta tion
(A student will read the objectives)
Before we proceed to the activity, short let us watch first the short video (The students will watch the short video clip presentation on angles of video clip presentation on angles of clip on elevation and angles of elevation and angles of depression) Angles depression.) of Eleva tion & Is the video clip on Angles of Depres Elevation and Angles of sion Depression clear to you? Yes Sir!
Let’s see, what is an angle of The angle of elevation is the angle elevation? between the imaginary line of sight and horizontal line, where the object is above the observer. What about depression?
an
angle
of The angle of depression is the angle between the imaginary line of sight and a horizontal line, where the object is below the observer.
Very well said. 15 mins
F. Activity 1. Pre-activity
For today’s activity, you will be working in groups which I previously assigned. We have four groups and each group will work on a specific problem. You need to choose a leader, two members who are in-charge in presenting an illustration of the given worded problem and two members who are in-charge in making the presentation of the solution using the Open Office Impress. The leader will be the one to facilitate the group and at the same time who will report the group output. Here are the rubrics in grading your group output: CRITERIA: Accuracy – 4 Cooperation – 2 Time Management – 2 Presentation – 2 TOTAL: 10 POINTS Note: Every group members are in-charge in solving for what is asked in the given problem.
Your activity is already saved in the computer desktop. The file name is Group Activity in Trigonometry. I will give you 10 minutes to finish the activity.
2. Activity Proper
Are you now ready to perform the group activity?
Yes Sir!
Group 1:
Group 1:
Problem: A bird sits on top of a Illustration: lamp post. The angle of ---------------35° depression from the bird to the feet of the observer standing ? away from the lamp post is 35 °. 14 ft. The lamp post is 14 ft. tall. How 35° far is the observer from the bird? Let x be the distance from the observer to bird.
Given: θ = 35°, opp. side = 14 ft. Unknown: x Equation: sin 35 ° = Solution: sin 35° =
x(sin 35°) = 14 x= x=
x = 24.4 ft. Answer: The distance from the bird to the feet of the observer is 24.4 ft. Group 2:
Group 2:
Problem: An airplane is flying at a height of 2 miles above the ground. The distance along the ground from the airplane to the airport is 5 miles. What is the angle of depression from the airplane to the airport?
Illustration: ----------------------------------x°
2 miles
x° 5 miles
Let x be the angle of depression from the airplane to the airport. Given: opp. side = 2 miles adj.side = 5 miles Unknown: x Equation:tan x ° = Solution:tan x° =
tan x° = 0.4 miles x° = tan-1(0.4) x° = 21.8° Answer: The angle of depression from the airplane to the airport is 21.8°.
Illustration, online scientific calculator, online Right Triangle Solver and slide presenta tion
Group 3:
Group 3:
Problem: A 20 ft ladder is leaning against a building. If the base of the ladder is 6 ft. from the base of the building, what is the angle of elevation of the ladder?
Illustration:
20 ft.
x° 6 ft. Let x be the angle of elevation of the ladder. Given: adj. side = 6 ft. hyp. = 20 ft. Unknown: x Equation: cos x ° = Solution: cos x ° =
cos x ° = 0.3 ft. x ° = cos-1(0.3) x ° = 72.54° Answer: The angle of elevation of the ladder is 72.54°. Group 4:
Group 4:
Problem: A tree casts a 12-meter Illustration: shadow where the angle of elevation of the sun is 25 °. How tall is the tree?
h=? 25°
12 m Let x be the height of the tree. Given: adj. side = 12 meters θ = 25° Representation: Equation: tan θ =
Solution: tan 25° =
x = (tan 25°)12 x = (0.4663)12 x = 5.5956 or 5.6 meters Answer:The height of the tree is 5.6 meters.
4 mins
3. Post-activity
Reporters, kindly group outputs.
present
the
G. Analysis
Let us analyze and briefly discuss the group activity that you’ve
(Reporters will present their outputs)
performed. In group 1, what are the given in the problem?
The given in the problem are the angle of depression from the bird to the feet of the observer standing away from the lamp post and the height of the lamp post.
How did you find the distance from the bird sitting on top of the lamp post to the feet of the observer?
We find the distance from the bird to the feet of the observer by applying the sine function.
In group 2, what are the given in the problem?
sin θ =
The given in the problem are the height of the airplane flying above the ground and the distance along the ground from the airplane to the airport.
How did you find the angle of depression from the airplane to We find the angle of depression from the airplane to the airport by the airport? applying the tangent function and the arctangent of the quotient of/ ratio of the opposite side and the adjacent side. In group 3, what are the given in the problem?
What trigonometric function did you used in solving for the angle of elevation of the ladder?
The given in the problem are the length of the ladder and the distance from the base of the ladder to the base of the building. The trigonometric function that we use in solving for the angle of elevation of the ladder is the cosine function (cos θ =
How did you find/solve for the angle of elevation of the ladder?
In the last group, what are the given in the problem?
What trigonometric function did you used in solving for the height of the tree?
).
We solve for the angle of elevation of the ladder by finding the arccosine of the ratio/quotient of the adjacent side and the hypotenuse. The given in the problem are the length of the shadow from the point on the ground to the base of the tree and the angle of elevation of the sun. Tangent Function.
How did you find the height of We find the height of the tree by the tree? equating the tangent of the given angle to the ratio of the unknown side to the adjacent side and by solving for the unknown which is the opposite side. 4 mins
H. Abstraction
What can you conclude about the appropriate trigonometric function to be used if the involved in any problem situation is the opposite side and the hypotenuse?
If the involved in a problem situation is the opposite side and the hypotenuse, the appropriate trigonometric function to be used is the sine function.
What about if the involved is the adjacent side and the hypotenuse?
If the involved in any problem situation is the adjacent side and the hypotenuse, the appropriate
trigonometric function to be used is the cosine function. How about if the involved in any problem situation is the opposite side and the adjacent side? What is the appropriate trigonometric function to be used?
If the involved in any problem situation is the opposite side and the adjacent side, the appropriate trigonometric function to be used is the tangent function.
In solving worded problems involving angle of elevation and depression, what are the useful steps involved?
The useful steps involved are: 1. Illustrate the problem situation. 2. Draw right triangle based on the problem situation. 3. Mark the known and unknown sides and angles. 4. Express the desired side or angle in terms of known trigonometric ratio. 5. Then solve for the unknown.
Very well said! 4 mins
5 mins
I. Application
J. Valuing/Relating
(The students will answer the online problem taken from this website:http://www.syvum.com/cgi/ online/fillin.cgi/math/trigo/trig3.tdf a They will illustrate the problem, write the Given, Unknown, Equation and the Solution in a layered-look book (foldable).
online problem layeredlook book (foldable)
Let’s relate the terms elevation and depression in real life. We have the term elevation, that term means rise which suggest going up or getting higher. Based on that term, how will you relate elevation/going up in real life as a student?
We can relate the term elevation/going up in real life in our studies in such away, that as students, we must study hard, do our best to succeed, elevate our life status to a higher degree in order for us to achieve our dreams and aspirations in life.
Thus, if you do your best and study hard, you will achieve all your dreams and aspirations in life, you will become successful and you will look up by other people. Do you agree?
Yes Sir, Just like the term elevation, we will be looked up by other people if we have already elevated our life status.
Great! So you are now on top/you are now elevated and since you are now on top/elevated, how will you relate now the term depression in real life if you are already successful?
We can relate the term depression in real life in such a way that if we are already on top/successful and have already achieved our dreams/aspirations; we must always look back or look down and stay humble at all times. Just like the term depression which always focuses on looking down to something.
Very well said! I do hope that just like the term elevation which suggests that when we are already on the top,
we must always remember to make a depression/look down to where we started. And I do hope that just like the term elevation which tells us that we must always go upward in life no matter how difficult the problems/challenges that we encounter. How about in solving worded problems involving angles of elevation and angles of depression? How can you relate the process of solving such in real life?
We can relate the process of solving such in real life that in every problem that we encounter, there is always a solution.
Exactly! All you need to do is to be positive always in dealing with problems/challenges in life. Do you have any questions and clarifications class regarding our lesson before we proceed to the online quiz? Please feel free to ask questions.
None Sir!
IV. EVALUATION (8 minutes)
The students will answer online problems involving angles of elevation and angles of depression taken from this website: http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-888484-5&chapter=8&lesson=5&&headerFile=7
V. ASSIGNMENT (2 minutes)
A. Solve the problem: A short building is 200 feet away from a taller building. Jessie is on the roof of the short building. To see the top of the taller building requires Jessie to look up with a 38 angle of elevation. To see the bottom of the taller building requires Jessie to look down with 12 angle of depression. Find the height of the taller building. (You may assume that Jessie’s height is negligible.)
B. Research and study about Law of Sines. Give example of solving problem involving oblique triangles using law of sines. Reference: Advanced Algebra by Soledad Jose – Dilao pages: 220-221.
Prepared by:
GENARO N. DE MESA, JR. Student Teacher
Checked by:
Noted:
NELIA B. ARIMADO Cooperating Teacher Chair, Sec. Educ. Program
NELIA A. BARCE Coordinator, LHS