Primary Trigonometric Ratios

Transcription

1 What s important in this lesson: Suggested time: 75 minutes Primary Trigonometric Ratios MFM2P1 Unit4 Lesson3 StudentinstructionSheet Questions for the teacher: 2. Assessment and Evaluation Sheet 1. The Student Handout. Hand-in the following to your teacher: 3. Check your lesson answer with the lesson key your teacher has. 5. Complete the Assessment and Evaluation and hand-in for evaluation. Be difficulty. sure to ask the teacher for any assistance when you are eperiencing any about the eamples. 4. Seek assistance from the teacher as needed, If you have any questions 2. Complete any of the eamples in the lesson. 1. Read through the lesson portion of the package independently. Complete these steps: of right triangles. In this lesson you will use trigonometry (sin,cos,tan) to measure sides and angles Student Instruction Sheet: unit 4 Lesson 3

2 hypotenuse hypotenuse adjacent = opposite adjacent tano = opposite We will be using our definitions from the last MFM2P1 Unit4 Lesson3 StudentHandout In this eample we will not solve the whole triangle. If you get a different value-check to make sure your calculator is in degrees. =13.9 =8 answers. 16(cos30 ) = 16(sin3O ) = sure you get the same cos30 = 16 your own calculator to make 16 sin3o Do these calculations on 0 X Now we set up a trig equation for each unknown side. (a) y makes the given angle it is also the side that with the hypotenuse 16cm We placed the (h) across from the right We placed the (a) on the remaining side angle. triangle. We placed the (o) across from the given angle it is also the longest side of the we know which ratio to use. The first step is to label the triangle with opposite (o), adjacent (a) and hypotenuse (h) so y 16cm the angle sum of a triangle. We will use trig ratios to solve for the remaining two side lengths. Eample 1. In this triangle we could quickly find the third angle which is 60 based on measure of all three angles. If we are asked to solve a triangle we have to find the length of all three sides and the that the angles in a triangle add up to 1800 to solve any right triangle. right triangle with sides a,b and hypotenuse h, we must have h2 = a2 + b2.) and the fact numbers which eactly give the side lengths of a right angle triangle we call these numbers a Pythagorean triple. Remember that the Pythagorean Theorem says that in a We can use these equations, the Pythagorean Theorem (if we have three whole Student Handout: Unit 4 Lesson 3

3 Student Handout: Unit 4 Lesson 3 Find the measure of the unknown angle to the nearest degree. 10cm 6cm The first step is to label the triangle with opposite (0), adjacent (a) and hypotenuse (h) so we know which ratio to use. 10cm We placed the (h) across from the right angle it is also the longest side of the triangle. We placed the (o) across from the given angle We placed the (a) on the remaining side 6 cm This time we are given no information about the opposite side so we are going to solve using the COSINE ratio. 6cm coso = 10cm 6 O=cos ( ) 10 P O53 means the inverse cosine (or the opposite operation to cos). We always use the inverse to find the angle. 1 sin is the inverse of sin 1 tan is the inverse of tan Note: If you are unable to and he!she will help you with get the your above calculator. answer please see your teacher MFM2P1 Unit4 Lesson3 StudentHandout

4 c) tan C = a) sin 23 c) tan 92 b) cos Evaluate each of the following trig ratios to four decimal places. Practice: MFM 2PR Unit 4 Lesson 3 B A 30mm C 5. Solve for. BA 5 cm 4. Solve for/c. BA Opposite 24cm C 3. Solve for. 2. Evaluate to find the angle to the nearest degree. a) sin A b) cos B = Student Handout: Unit 4 Lesson 3

5 Student Handout: Unit 4 Lesson 3 6. Solve for/b. 54 mm B A 7. Solvefora. cm B A 8. Solve for ZC. C B 20 cm A 9. Solve for. 12cm N \15 cm Ii MFM 2PR Unit 4 Lesson 3

6 2. Evaluate to find the angle to the nearest degree. a) tan A = b) sin B c) cos C = 3 5 MFM 2PR Student Assessment Unit 4 Lesson Solve for to the nearest degree Find the side length to one decimal place. Student Assessment: Unit 4 Lesson Evaluate each of the following trig ratios to four decimal places. 50 a) cos 23 b) tan 18 c) sin 32 5