- 1. LESSON PLAN FOR MATHEMATICS 9 I. INFORMATION Subject Matter: Law of Sines Grade Level: IX Time Allotment: 1 hour Teacher/s: Elton John B. Embodo Content Standard: The learner demonstrates understanding of the basic concepts of trigonometry. Performance Standard: The learner is able to apply the concepts of trigonometric ratios to formulate and solve real life problems with precision and accuracy. Learning Competency: The learner solves problems involving oblique triangles. M9GE-IVh-j-1 Objectives: At the end of the lesson, the students must have: a. solved problems involving oblique triangles using the law of sines; and b. discussed the importance of obedience with the law. References: Hayden, J. R. & Hall, B. C. (1999). Trigonometry. Anvil Publishing, Inc. ISBN 971-27-0435-1 Instructional Materials: PowerPoint, chalk Skills: Analysis and Collaboration Values: Unity, cooperation, camaraderie Method: Developmental Method II. LEARNING EXPERIENCES Teacher’s Activity Students’ Response A. Preparation 1. Prayer 2. Greetings 3. Reminders 4. Checking of Attendance 5. Classroom Rules - MATH M - must come to class neat, clean, and prepared. A - actively participate in the activities and pay attention to the discussion. T - talk appropriately and respectfully to your teacher and classmates. H - handle the learning materials with care. Are my rules clear to you class? a. Review In solving problems involving right tringles, we use trigonometric ratios of Sine, Cosine, and Tangent. What is the trigonometric ratio of Sine? How about the Cosine? How about the Tangent? I have here few problems. I need volunteers to answer. Yes Sir! Sin opposite hypotenuse or SOH. Cos adjacent hypotenuse or CAH Tan opposite adjacent or TOA
- 2. Directions: Find the value of x using the appropriate trigonometric ratios. 1. 2. 3. b. Motivation I have here two triangles namely triangle ABC and triangle XYZ. How do you describe the triangle ABC? Why did you say that it is an acute? How about the second triangle XYZ? Why is that? Tan 20 13 O x 13Tan 20 4.73 O x x Cos41 14 O x 14Cos 41O x 10.57 x Sin 65 25 O x 25Sin 65O x 22.66 x I think that the triangle ABC is acute. It is because all its angles are acute. The second triangle is obtuse. x 20O 13 41O 14 x x 65O 25 C A B a b c X z Y Z y x
- 3. In short class, these triangles are oblique. In your previous lesson class, you solved problems involving right triangles using the trigonometric ratios. But how about if the problems involve oblique triangles? How do we solve those problems? B. Presentation So be with me this morning class as we tackle another lesson which is the Law of Sines. Everybody read! Statement of the Aim Listen very attentively since you are expected to achieve these objectives. Everybody read! C. Development Proper The Law of Sines is used in solving problems involving oblique triangles when a. Two angles and one side are given b. Two sides and an opposite angle of one of them are given. In a triangle ABC, The law of sines is expressed as sin sin sin A B C a b c This is read as sine of angle A over the opposite side a is equal to sine of angle B over the opposite side b is equal to sine of angle C over the opposite side c. Giving of Examples It is because it has one obtuse angle. Law of Sines Objectives: a. solve problems involving oblique triangles using the law of sines; and b. discuss the importance of obedience with the law. 1. Suppose that a parcel of land is triangular, with vertices A and B on the roadway and the third vertex marked at point C. A surveyor measures the distance from A and B and finds that it is 245.8 ft. The lines of sight from A and B to C makes angles 79.46O and 51.67O , respectively with the line from A to B. Find the following. a. Angle C b. Distance from point A to C or side b c. Distance from point B to C or side a d. Area of the triangular parcel of the land. A B C b a c
- 4. Concept Integration Now class, before we are going to solve the problem, what other learning areas you can associate the problem with? Is there anyone here who has an idea about surveying? Have you ever seen someone doing the surveying of a certain land? Very good! That apparatus class is called theodolite together with the other instruments. Since one of the things to find class is the area of the parcel of a land, what branch of mathematics class that usually deals with finding an area of a plane figure? Fabulous! Solution to the problem The first thing to do class is to sketch the problem. Is there anyone here would like to do it on the board? a. How are we going to solve for angle C? Any volunteer? b. To solve for the distance from point A to C or the side b, we will now make use of the Law of Sine. sin sin B C b c sin51.67 sin 48.87 245.8 O O b (sin 48.87 ) 245.8(sin51.67 ) O O b (sin 48.87 ) 245.8(sin51.67 ) (sin 48.87 ) (sin 48.87 ) O O O O b 255.99 b ft The problem sir is related to civil engineering since it specifically mentioned about surveying. Surveying for me sir is a technique of assessing and recording details about an area of the land. Yes sir, he uses an apparatus that looks like a camera. It is Geometry sir since it deals with the perimeter, area, surface area and volume of plane or solid figures. (The possible sketch of the problem is drawn on the board) 180 79.46 51.67 180 131.13 48.87 O O O O O O C C C 245.8 79.46O 51.67O A B C b a
- 5. c. Following the same process class, who would like to solve for the distance from point B to C or the side a? d. To solve for the area of a triangular parcel of a land, we will use the formula involving 2 sides of a triangle and an included angle. 1 sin 2 Area ab C 1 (320.83 )(255.99 )sin 48.87 2 O Area ft ft 2 30930.67 Area ft Values Integration Okay, we have solved one problem involving an oblique triangle. What law again class that we followed or used in solving the first problem a while ago? Perfect, we used the law of sine to solve the first problem. Class, in your real-life experiences, why is it important to follow the laws in our society? Absolutely! If we do not follow the laws, we will face some consequences and we do not want to experience it. We must obey them so that we will live our lives peacefully and harmoniously. Collaborative Activities To have a better and deeper understanding on how solve problems involving oblique triangles using the law of sines, we will have a group activity. Here are the mechanics. sin sin A C a c sin79.46 sin 48.87 245.8 O O a (sin 48.87 ) 245.8(sin79.46 ) O O a (sin 48.87 ) 245.8(sin79.46 ) (sin 48.87 ) (sin 48.87 ) O O O O a 320.83 a ft We used the law of sine sir. It is very important to follow the laws sir in our society since the laws are made to regulate the actions of the people to bring peace and order in the society.
- 6. Prepared: Presentation and Verification of Group Outputs (The two groups solve the given problem) III. EVALUATION Directions: In a one whole sheet of paper, solve the following problems involving oblique triangles using the law of sines. 1. From a point A, the angle of elevation to the top of a tree (point T) is 38 degrees. From a point B 25 ft closer to the three, the angle of elevation to the top is 48 degrees. How far is it from point B and T? how tall is the tree? Express your answers to the nearest foot. 2. A flagpole stands on the edge of the bank of a river. From a point on the opposite bank directly across from the flagpole, the measure of the angle of elevation to the top of the pole is 25 degrees. From a point 200 ft further away and in line with the pole and the first point, the measure of the angle of elevation to the top of the pole is 21 degrees. Draw a diagram. Then find the distance across the river. 3. If a pole has one 62-ft guy wire that makes an angle of 39 degrees with the ground, and a second 50-ft guy wire is available for the opposite side of the pole, what angle measure will the second wire make with the ground? IV. ASSIGNMENT Directions: Read in advance on how to use the law of cosines in solving problems involving oblique triangles. 1. The class will be divided into two groups. 2. Each group will be given with the same problem to be solved in 5 minutes. 3. The group which can finish solving the problem first with correct solutions and answers will be declared as the winner. 4. Each group must select one representative to explain the output in front. Example 2 From two points P and Q that are 140 ft apart, the lines of sight to a flagpole across a river make angles of 79O and 58O , respectively, with the line joining P and Q. What are the distances from P and Q to the flagpole? 58O P Q 79O 140 ft
- 7. ELTON JOHN B. EMBODO, MAED, LPT Teacher Applicant