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Mathematics – Grade 9 Quarter 4 – Self-Learning Module 3: Solving a Right Triangle Given the Length of the Hypotenuse and Measure of One Acute Angle First Edition, 2020
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Measure of One Acute Angle
Length of the Hypotenuse and
Solving a Right Triangle Given the
Self- Learning Module 3
Quarter 4
Mathematic s
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Published by the Department of Education - Schools Division of Pasig City Development Team of the Self-Learning Module Writer: Joan Magapi; Frank Luther Gordon 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
Introductory Message
For the Facilitator: Welcome to the Mathematics Grade 9 Self-Learning Module on Solving a Right Triangle Given the Length of the Hypotenuse and Measure of One Acute Angle! 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:
As a facilitator you are expected to orient the learners on how to use this selflearning 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.
will help you in guiding the learners.
This containshelpful tips or strategies that
Notes to the Teacher
For the Learner: Welcome to the Mathematics Grade 9 Self-Learning Module on Solving a Right Triangle Given the Length of the Hypotenuse and Measure of One Acute Angle!
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 self-learning 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 self-learning 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 self-learning module.
In right triangle ΔEFG, find:
In right triangle ΔBCD, find:
This lesson deals with the second case of solving right triangles. Again, solving a right triangle means finding the measure of its parts. This time, given are the length of the hypotenuse and the measure of one acute angle.
LESSON
RECAP
5 .m∠ D
m∠ B
length of GF
2 .m∠ E
- m∠ G
Direction:Findthe missing parts in each right triangle.
The right triangle ΔABC above has ̅𝐴𝐶̅̅̅̅̅̅ as its hypotenuse and ∠C as its one acute angle. Can you tell the missing parts in this right triangle?
To determine its missing parts, remember that a triangle has three sides and three angles. See the table below.
THREE SIDES THREE ANGLES ̅𝐴𝐶̅̅̅̅̅̅ (hypotenuse) - given ∠A (an acute angle) – missing ̅𝑨𝑩̅̅̅̅̅̅ (one of the legs) - missing ∠B (right angle) – given ̅𝑩̅̅̅ 𝑪̅̅̅̅̅̅ (one of the legs) - missing ∠C (acute angle) – given
So, in this case, the missing parts are the two legs of the right triangle and its one acute angle.
EXAMPLE.
Find the measurement of the missing parts of the right triangle ΔQSR.
Solution: Given: s = 28 - hypotenuse m ∠Q = 40° - acute angle
Missing Parts (one acute angle and two legs):
- m ∠R =?
- r =?
- q =?
- Find R To find R, remember that the two acute angles of a right triangle are complementary; that is, their sum should be 90°. m R + m Q = 90° m R = 90°– m Q m R = 90°– 40° m R = 50°
- Find r.
By looking at the figure, side r is adjacent to Q, and side s is the hypotenuse. To solve r , use CAH (cosine-adjacent-hypotenuse). 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 cos 𝑄 = ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑟 cos Q = 𝑠 𝑟 cos 40° = 28 r = 28 cos 40° r = 28 (0.7660)
ACTIVITY 3: TEST YOURSELF! Direction: Using the same right triangles in Activity 2, find the value of each indicated missing part, round off your answers to two decimal places.
17 m = 17 sin 56° m = 17 (0.8290) m = 14.
(example )
43 ° 31
I^ f =?
F
X
34 °
10
b =?
B
A C
m =?
(^1756) °
L
N
M
2. side b 3. side f
sin 56 ° =^ 𝑚
17 sinQ =^ 𝑚
ℎ 𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 sin𝑀 =^ 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
1 .side m - SOH
Direction: Answer the following questions:
- What does it mean to solve a right triangle?
- How do you solve a right triangle given the length of its hypotenuse and the measure of one acute angle?
REFLECTION: (Journal Writing)
The lesson tells us that solving right triangles means finding the measures of its missing parts. For us to completely describe the right triangles, one must find the measure of each of its sides and angles. The measures may not be that very exact, but we use defined formulas to find its estimated values. We can relate the concept of ‘finding the missing parts of right triangles to one of the best quotations of Mr. Carl Jung, “Life calls, not for perfection, but completeness.” What do you think are the things or qualities that may make a person’s life complete?
48 °
y=?
F L
Y
43 °
p =?
40
I
T P
25 °
26
T
E
t=?
S
4. side t 5. side p 6. side y
WRAP- UP
VALUING
