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IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig (A) Lesson Context BIG PICTURE of this UNIT: Working with a more comprehensive Trig Unit from right triangle to nonright triangle trig. Working with Sinusoidals Where we’ve been CONTEXT of this LESSON: Where we are Just finished up Reviewing the concepts Polynomials. We has of right triangle trig. seen the basics of right triangle trig in IM 2 Where we are heading A lot of places. Task 1: Solving for Angles, Lengths, and Distances Task 2: Three types of Trigonometry Questions: Task 3: Trigonometric Ratios in Complex Situations and Real World Situations IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig Task 1: Solving for Angles, Lengths, and Distances Review of Pythagorean Theorem: The Pythagorean Theorem can be used to solve the lengths of missing sides in right triangles. Example 1: Find the value of the hypotenuse, h. Example 2: Find the missing side, s, using the Pythagorean Theorem. 6.4 cm Practice: Find the missing side, s. 2.2 cm IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig Trigonometric Ratios: There are three trigonometric ratios that can be used to problems of right triangles. Recall: You will need to be able to solve right triangles for all missing sides and angles. solve IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig Task 2: Three types of Trigonometry Questions: 1. Solving for the top of the ratio Solve for c: A c 55º 6.5 cm B C X 6.4 cm z Practice: Solve for the missing side, z. 35º 6.2 ft Y Z IM 3 Lesson 5.1 : Right Triangle TrigX Unit 5 – Trig 2. Solving for the bottom of the ratio z Solve for z: 65º Z Practice: Solve for a: Y 6 ft A 4.3 cm 25º B a C IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig 3. Solving for the angle Solve for angle G: F 11.2 ft H Worksheet: Trigonometric Ratios Trigonometric Ratios Worksheet 1. Determine the value θ of to four decimal places. (a) (b) 7.3 ft G IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig © 2. Find the height, h, of the triangle to one decimal place. 3. Calculate the length of the indicated side. (a) (b) IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig c) (d) (e) (f) Answers: 1. a) 32.7117º b) 51.5001º c) 44.7913º 2. 16.7cm 3. a) 4m b) 12.2cm c) 8.6cm d) 12.5m e) 3.6 cm f) 2.4m IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig Task 3: Complex Situations Trigonometric ratios can be used to solve real-life situations; these calculations may require multiple steps. Example: Solve for QS, ST, and RT. Worksheet: Trigonometric Ratios and Complex Problems Note: the sum of the angles in a triangle is 180º. IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig Trigonometric Ratios and Complex Problems Worksheet 1. What is the length of x? 2. Calculate the measure of angle θ. IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig 3. Find each of the indicated sides. 4. A ladder placed against a wall forms an angle of 65° with the ground. If the foot of the ladder is 1.8 m from the wall, how long is the ladder? IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig 5. Pauline is building a fence around her vegetable garden, shown below. What length of fence will she need to build? 6. A surveyor must determine the distance, across a river. He stands at point C, downriver 500 m from B, measures the angle of vision to A as 28°. How wide is the river? AB, IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig Answers: 1. 35.6 cm 2. 54º 3. 7.1 m; 3.7 m 4. 4.3 m 5. 11.94 m 6. 265.9 m 5.2 Solving Complex Problems in the Real World More complex problems may require you to break down the problem into two or more triangles with work through several steps. You can use the values from one triangle in the other if they share a common edge. Example 1: Solve for x and y in the following diagram. Worksheet: Working with Two Triangles Working with Two Triangles Worksheet IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig 1. Calculate x in the following diagram. 2. Find x and y in the following diagrams. IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig 3. Calculate x, y, and h for the following diagram. Answers: 1. 5.2 m 2. a) 12.7 cm; 19.0 cm b) 11.6 m; 10 m 3. 17.1 cm; 6.4 cm; 8.5 cm IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig Example 2: A flagpole is supported by two guy wires, each attached to a peg in the ground 4 m from the base of the pole. The guy wires have angles of elevations of 35° and 45°. a) How much higher up the flagpole is the top guy wire attached? b) How long is each guy wire? Worksheet: Real-Life Trigonometry Problems Project: Real-World Trigonometry Real-Life Trigonometry Problems Worksheet IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig 1. From the top of a 200 m-tall office building, the angle of elevation to the top of another building is 40°. The angle of depression to the bottom of the second building is 25°. How tall is the second building? 2. A roller drops at an from a reaches the horizontally angle of of 26.8 m. coaster has a track that angle of depression of 25° height of 14.9 m. When it ground, in travels for 8 m. It then rises at an elevation of 47° to a height IM 3 Lesson 5.1 : Right Triangle Trig Unit 5 – Trig a) What is the total horizontal distance covered by this portion of track? b) What is the total distance travelled by a car on this portion of the roller coaster track? Answers: 1. 560 m 2. a) 65 m b) 82.6 m