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Topic Prerequisite Skills 1.1 Revisit the Primary Trig Ratios 1.2 Solve Problems Using Trig Ratios 1.3 The Sine Law 1.4 The Cosine Law 1.5 Make Decisions Using Trig Review Test Assigned Work Pg 4-5 #1-10 Pg 13-15 #1-12 Pg 21-23 #1-6, 8, 11-15 Pg 31-33 #1-3, 5, 8, 9 Try 13!! Pg 39-41 #1-5, 7-10, one of 11-13 Pg 48-51 #1, 2abc, 3, 4, 6-8, 10, 11, one of 12-14 Pg 52-53 #1-9, 12-17 Pg 54-55 #1-9 Pg 58-59 #1-5, 7-10 Done Learning Goals: By the end of this unit, students will be able to solve right-angled and acute triangles using appropriate trigonometric strategies. Students will be able to extend this knowledge to solve real-life application problems. Prerequisite Skills Example 1. Solving Equations with Squared Variables X2 - 27 = 9 x2 + 52 = 72 How to Label Triangles Example 2. The Pythagorean Theorem A A 10 m 7 cm C c C B 14 m a 5 cm B Example 3. Ratios and Proportions a) Express in lowest terms 5:10 8: 18 b) Solve for the unknown x:5 = 4:20 3:10 = 60:y Hint for lowest terms: any number where the last digit is even can be divided by 2 AND any number where the last digit is 5 or 0, can be divided by 5! Example 4. Rounding a) Round to the nearest unit 10.4 150.78 5.589 b) Round to the nearest tenth 12.384 4.65 5.993 Example 5. Angle Sum of a Triangle The sum of the angles within a triangle is always _________. Determine the measure of the missing angles. Homework Pg 4-5 #1-10 1.1 Revisit the Primary Trigonometric Ratios What we know: -if we are given two sides of a right-angled triangle, we can find the length of the unknown side using Pythagorean theorem Do we remember? In grade 10, you learned that you can find sides and angles of a right-angled triangle if you were given either two sides OR 1 side and 1 angle. You used: SOH CAH TOA Θ called “theta” – represents the angle The hypotenuse is always opposite the right angle (and is the longest side!), but the opposite and adjacent sides are identified from the reference angle. Θ Θ Homework Pg 13-15 #1-12 1.2 Solving Problems with SOH CAH TOA 1. Write the 3 equations for SOH CAH TOA 2. Describe how you know when to use SOH CAH TOA . . . 3. What are the steps for SOH CAH TOA? 1. Label sides HYP, OPP, ADJ 2. Decide SOH CAH or TOA (circle what you need & what you have -> these sides need to be in the one you pick!) 3. Write the equation and solve for the unknown (you can write it over 1 and use cross multiply and divide) 4. Need to find an angle? use sin-1, cos-1, tan-1 check that you can do it: □ 4. Complete “Warm UP” handout. Let’s try an example of when we can use this trigonometry in real life . . . (see text pg. 18) We will answer this question on back – start by drawing a picture!! 4. What is an “angle of depression”?? 7. What is an angle of inclination?? Homework Pg 21-23 #1-6, 8, 11-15 1.3 Non-Right Angle Triangles – Sine Law Have texts open to page 31 (your homework is on the back of this sheet) Your Turn! Do Q #1, pg. 31 and check your answer in the back of the book. Help someone else if you get it right! Your Turn! Do Q #2, pg. 31 and check your answer in the back of the book. Help someone else if you get it right! Homework Pg 31-33 #1-3, 5, 8, 9 Try 13!! 1.4 The Cosine Law You can also solve a triangle if you know the following: - Find a side: given the other two sides and their contained angle - Find angle: given the three sides Homework Pg 39-41 #1-5, 7-10, one of 11-13 1.5 Making Decisions Using Trigonometry Like always, when it comes to problem solving you need to fully read the problem, highlight key information, and draw a diagram to help you decide what method you will use to solve it. You can use the flow chart below to help you decide. Trigonometry Problem Right-angled Triangle Acute Triangle Sine Law Pythagorean Theorem Given 2 angles and a side sin cos Cosine Law Given 2 sides and a contained angle tan Given 2 sides and an angle opposite one of them Given 3 sides Homework Pg 48-51 #1, 2abc, 3, 4, 6-8, 10, 11, one of 12-14 Unit Review Review Pg 52-53 #1-9, 12-17 Pg 54-55 #1-9 Unit Test Homework after unit test (prep for unit 2!) Pg 58-59 #1-5, 7-10