Lesson exemplar in writing the equation needed in solving the right triangle
- 1. Lesson Exemplar in Mathematics 9 Lesson: Solving Right Triangle by using Trigonometric Ratios Grade Level: Grade 9 Grading Period: Fourth Quarter Learning Competency: Determining what formula/equation is needed in solving the missing part of a right triangle. Duration: 1 session A. RECALL: Parts of a Right triangle Questions: What is called to perpendicular sides of a right triangle? Answer: legs What is called to the slanting side of a right triangle? Answer: hypotenuse The Six Trigonometric Ratios Questions: What is reference angle? Answer: It is an angle use to identify the specified term for the legs of a right triangle, the opposite side and the adjacent side. It may be θ, A, B or any capital letter of the English alphabet. How do you know the opposite side in a right triangle? Answer: It is the side opposite the reference angle. How do you know the adjacent side in a right triangle? Answer: It is the side adjacent to the refence angle other than the hypotenuse. What are the 6 trigonometric ratios? Answer: Sine θ, Cosine θ, Tangent θ, Cosecant θ ,Secant θ and Cotangent θ. What is sine θ? Answer: sin θ = opposite/hypotenuse What is cosine θ? Answer: cos θ = adjacent/hypotenuse What is tangent θ? Answer: tan θ= opposite/adjacent What is cosecant θ? Answer: csc θ = hypotenuse/opposite What is cotangent θ? Answer: cot θ = adjacent / opposite What is secant θ? Answer: sec θ = hypotenuse/adjacent How do you find the measure of A, if sin A = 0.3456? Answer: Enter shift sin 0.3456 What is the value of A ,if sin A = 0.3456? Answer: 20.220
- 2. c = 23a b=17 B C A A = 42.34⁰ B = 47.66⁰ a = 15.49 CosA= === Cos A = A tower is 15.24 m high. At a certain distance away from the tower, an observer determines that the angle of elevation to the top of it is 41⁰. How far is the observer from the base of the tower. B.DISCUSSION: To determine the trigonometric ratio use in solving the missing parts of a right triangle, follow these steps: a. Understand, analyze, then draw the triangle, if triangle is not yet drawn and label it correctly. b. Know what is the reference angle. c. Identify the given parts and know what is to find for. d. Choose the appropriate trigonometric ratio needed to solve the missing parts of a right triangle. Examples: 1. Triangle BCA is right- angled at C. If a=23 and b=17, find A, B and a. Express your answer in two decimal places. Understand, then sketch the problem. Reference angle: A or θ opposite side: a=? adjacent side: b=17 hypotenuse: c =23 Acute angles: A=? ,B=? In solving A, the reference angle, use cosine since the given sides are adjacent and hypotenuse. adjacent side 17 A =cos-1 17 hypotenuse 23 23 Since mA + mB + mC = 180 in any triangle, therefore mB = 180- (mA + mC) In finding a, there are two possible trigonometric ratios to use, either tangent or sine. Using sin A = opposite side/hypotenuse; sin 42.35 = a/23 a = 23(sin42.35) Using tan A= opposite/adjacent ; tan 42.35 = a/17 a=17(tan 42.35) You will notice that the values of a are equal since we are referring to the same triangle, if you try to find the value of a. 2. B
- 3. Tan 410 = A 410 C X or opposite side 15.24 adjacent side X X= 𝟏𝟓.𝟐𝟒 𝑻𝒂𝒏 𝟒𝟏 C. ASSESSMENT Write the formula needed in solving the missing parts of a right triangle for each problems below. A. For numbers 1 to 5, use the figure below B 1. If a=5 and c=10,find the measure of A. a c 2. If b=7 and c= 12,find the measure of A. 3. If a= 8 and b = 10, find the measure of A. C A 4. If the measure of A =700 and c= 15, find a. b 5. If the measure of B =630 and b= 15, find a. B. From the top of a cliff 280m high, the angle of depression of a boat is 700. How far from the base of the cliff is the boat? RUBRICS: Task: Writingthe formula that isneededtosolve the missingpartsof the righttriangle. Points 3 1 0 Criteria The answeris correct. The answeris wrong. No attempttoanswer. 15.24m Since 15.24 is opposite the given angle,410 ,andthe missingside isX, the adjacentside, the trigonometricratioto use istangent.Rememberthe mnemonicsSOH-CAH-TOA. Tan A=