Transcript trig ratios
Right Triangle Triginometry A Stand-Alone Instructional Resource Created by Lindsay Sanders Standards & Objectives Students in Mathematics II will be able to• Discover the relationship of the trigonometric ratios for similar triangles. • Explain the relationship between the trigonometric ratios of complementary angles. • Solve application problems using the trigonometric ratios. Introduction • This project is a tutorial for learning how to solve right triangles using basic trigonometry. • You will learn vocabulary, participate in minilessons, and answer questions based on what you learned. • You will need a scientific calculator or use an online scientific calculator • At the end of this tutorial, there are links to online resources for right triangle trigonometry, including applets and games. Vocabulary • Hypotenuse- the longest side, opposite of the right angle • Opposite side- the side opposite of the chosen angle • Adjacent side- the side touching the chosen angle To learn more, please watch this video opposite adjacent Trigonometric Ratios Click on the trigonometric ratios below to learn more. Sine Cosine Tangent Sine • A trigonometric ratio (fraction) for acute angles that involve the length of the opposite side and the hypotenuse of a right triangle, abbreviated Sin B opposite Click for trig ratios Click for example C A length of leg opposite A BC Sin A = = AB length of hypotenuse Example 1 Find Sin A. opposite BC Sin A = hypotenuse = AB B 25 15 A C 20 15 = 25 3 = 5 = 0.60 Click for trig ratios Click for practice You try! Find Sin A. B 53 A 45 28 C 28 (a) = 0.62 45 No this ratio is opposite over adjacent 28 Yes this ratio is (b) = 0.53 opposite over hypotenuse 53 45 this ratio is adjacent (c) = 0.85 No over hypotenuse 53 53 (d) = 1.89 No this ratio is hypotenuse over opposite 28 Back to Click for example trig ratios Click for another You try! Find Sin B. B 24 C 26 10 A 10 (a) = 0.42 24 No this ratio is opposite over adjacent 24 (b) = 0.92 26 No this ratio is adjacent over hypotenuse 24 (c) = 2.40 10 No this ratio is adjacent over opposite 10 Yes this ratio is (d) = 0.39 opposite over hypotenuse 26 Back Click for trig ratios Click for Cosine Cosine • A trigonometric ratio for acute angles that involve the length of the adjacent side and the hypotenuse of a right triangle, abbreviated Cos B Click for example Click for trig ratios C adjacent A length of leg adjacent A AC Cos A = = length of hypotenuse AB Example 2 Find Cos A. adjacent AC Cos A = = AB hypotenuse B 20 = 25 25 15 A C 20 4 = 5 = 0.80 Click for trig ratios Click for practice You try! Find Cos A. 37 A 12 B 12 (a) = 0.32 37 35 35 (b) = 0.95 37 C Back to Click for example trig ratios Click for another Yes this ratio is adjacent over hypotenuse No this ratio is opposite over hypotenuse 35 (c) = 2.92 12 No this ratio is opposite over adjacent 12 (d) = 0.34 35 No this ratio is adjacent over opposite You try! Find Cos B. A 36 85 C 77 B Back Click for trig ratios Click for Tangent 36 (a) = 0.42 85 No this ratio is opposite over hypotenuse 36 (b) = 0.47 77 No this ratio is opposite over adjacent 77 (c) = 0.91 85 Yes this ratio is adjacent over hypotenuse 85 (d) = 1.10 77 No this ratio is hypotenuse over adjacent Tangent • A trigonometric ratio for acute angles that involve the length of the opposite side and the adjacent side of a right triangle, abbreviated Tan B opposite Click for example Click for trig ratios C adjacent A length of leg opposite A BC Tan A = = length of leg adjacent AC Example 3 Find Tan A. BC opposite Tan A = adjacent = AC B 15 = 20 25 15 A C 20 3 = 4 = 0.75 Back Click for trig ratios Click for practice You try! Find Tan A. C 40 B 42 58 42 (a) = 1.05 40 No this ratio is adjacent over opposite 42 (b) = 0.72 58 No this ratio is adjacent over hypotenuse 40 (c) = 0.69 58 No this ratio is opposite over hypotenuse 40 (d) = 0.95 42 Yes this ratio is opposite over adjacent A Back Click for trig ratios Click for another You try! Find Tan B. B 15 A 9 12 12 (a) = 1.33 9 Yes this ratio is opposite over adjacent 9 (b) = 0.60 15 No this ratio is adjacent over hypotenuse 12 (c) = 0.80 15 No this ratio is opposite over hypotenuse C 9 ratio is adjacent (d) = 0.75 No this over opposite 12 Back Click for trig ratios Click to go on Solving for a Side Length In order to solve for x, you will need to use one of the trigonometric ratios you just learned about! x 42˚ Click for trig ratios Click for example Example 4 Solve for x. Step 1. Decide what type of sides are given. x – opposite 52 – hypotenuse Step 2. Decide what trig function to use. Sine! It is opposite over hypotenuse! Step 3. Set up the ratio and solve for x. x 52 · Sin 42˚ = 42˚ x · 52 52 34.8 = x Multiply both side by 52 Put 52 · sin 42 in calculator Back Click for Click for trig ratios practice You try! Solve for x. 39˚ x Back Click for Click for trig ratios answer answer: x = 10.1 Back Click for Click for trig ratios another You try! Solve for x. 31˚ x Back Click for Click for trig ratios answer answer: x = 8.6 Back Click for Click for trig ratios another You try! Solve for x. x 44˚ 23 Back Click for Click for trig ratios answer answer: x = 22.2 Back Click for trig ratios Click for more For more information… @Home Tutor – Right Triangle Trig YourTeacher – Solving for sides using Trig video Right Triangle Calculator and Solver This Stand Alone Instructional Resource was created using PowerPoint. All sounds are also from PowerPoint. Information, definitions, and examples were adapted from in McDougall Littell’s Mathematics 2 textbook. Click to start over