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Mastering Right Triangle Trigonometry Tutorial

This stand-alone instructional resource by Lindsay Sanders teaches how to solve right triangles using basic trigonometry. Students will discover trigonometric ratios for similar triangles, explain ratios for complementary angles, and solve application problems. The tutorial includes vocabulary, mini-lessons, interactive questions, and links to online resources. Learn about sine, cosine, tangent, and how to find side lengths using trigonometric functions. Practice solving for x and gain a solid understanding of right triangle trigonometry concepts.

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Mastering Right Triangle Trigonometry Tutorial

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  1. Right Triangle Triginometry A Stand-AloneInstructional Resource Created by Lindsay Sanders

  2. 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.

  3. Introduction • This project is a tutorial for learning how to solve right triangles using basic trigonometry. • You will learn vocabulary, participate in mini-lessons, 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.

  4. Vocabulary • Hypotenuse- the longestside, opposite of the right angle • Opposite side- the sideopposite of the chosen angle • Adjacent side- the sidetouching the chosen angle hypotenuse To learn more, please watch this video opposite adjacent

  5. Trigonometric Ratios Click on the trigonometric ratios below to learn more. Cosine Sine Tangent

  6. Sine • A trigonometric ratio (fraction) for acute angles thatinvolve the length of the opposite side and the hypotenuse of a right triangle, abbreviated Sin B hypotenuse opposite Click for trig ratios Click for example C A length of leg opposite A BC Sin A = = AB length of hypotenuse

  7. Example 1 opposite BC Find Sin A. Sin A = = B hypotenuse AB 15 25 15 = 25 3 = A C 5 20 = 0.60 Click for trig ratios Click for practice

  8. You try! 53 28 28 45 No  this ratio is opposite over adjacent (d) = 1.89 (a) = 0.62 Find Sin A. B 28 53 53 Yes  this ratio is opposite over hypotenuse (b) = 0.53 28 45 53 No  this ratio is adjacent over hypotenuse A C (c) = 0.85 45 No  this ratio is hypotenuse over opposite Click for trig ratios Click for another Back to example

  9. You try! 10 26 10 24 No  this ratio is opposite over adjacent (d) = 0.39 (a) = 0.42 Find Sin B. B 24 26 No  this ratio is adjacent over hypotenuse (b) = 0.92 26 24 24 10 No  this ratio is adjacent over opposite (c) = 2.40 A C 10 Yes  this ratio is opposite over hypotenuse Click for trig ratios Click for Cosine Back

  10. Cosine • A trigonometric ratio for acute angles thatinvolve the length of the adjacent side and the hypotenuse of a right triangle, abbreviated Cos B hypotenuse Click for example Click for trig ratios C A adjacent AC length of leg adjacent A Cos A = = length of hypotenuse AB

  11. Example 2 adjacent AC Find Cos A. Cos A = = B AB hypotenuse 20 25 = 15 25 4 A C = 20 5 = 0.80 Click for trig ratios Click for practice

  12. You try! 12 35 12 37 Yes  this ratio is adjacent over hypotenuse (d) = 0.34 (a) = 0.32 Find Cos A. B 35 37 No  this ratio is opposite over hypotenuse (b) = 0.95 37 35 35 12 No  this ratio is opposite over adjacent C A (c) = 2.92 12 No  this ratio is adjacent over opposite Click for trig ratios Click for another Back to example

  13. You try! 85 77 36 85 No  this ratio is opposite over hypotenuse (a) = 0.42 (d) = 1.10 36 Find Cos B. C A 36 77 No  this ratio is opposite over adjacent 77 (b) = 0.47 85 77 85 Yes  this ratio is adjacent over hypotenuse (c) = 0.91 B No  this ratio is hypotenuse over adjacent Click for trig ratios Click for Tangent Back

  14. Tangent • A trigonometric ratio for acute angles thatinvolve 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 A adjacent length of leg opposite A BC Tan A = = length of leg adjacent AC

  15. Example 3 BC opposite Find Tan A. Tan A = = adjacent AC B 15 25 = 15 20 3 A = C 20 4 = 0.75 Click for trig ratios Click for practice Back

  16. You try! 42 40 40 42 No  this ratio is adjacent over opposite (a) = 1.05 (d) = 0.95 40 Find Tan A. C B 42 42 58 No  this ratio is adjacent over hypotenuse 58 (b) = 0.72 A 40 58 No  this ratio is opposite over hypotenuse (c) = 0.69 Yes  this ratio is opposite over adjacent Click for trig ratios Click for another Back

  17. You try! 9 12 12 9 Yes  this ratio is opposite over adjacent (d) = 0.75 (a) = 1.33 Find Tan B. B 15 9 9 15 No  this ratio is adjacent over hypotenuse (b) = 0.60 C A 12 12 15 No  this ratio is opposite over hypotenuse (c) = 0.80 No  this ratio is adjacent over opposite Click for trig ratios Click to go on Back

  18. Solving for a SideLength In order to solve for x, youwillneed to use one of the trigonometric ratios youjustlearned about! 52 x 42˚ Click for trig ratios Click for example

  19. 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. 52 x x 52 · Sin 42˚ = · 52 Multiply both side by 52 52 42˚ Put 52 · sin 42 in calculator 34.8 = x Click for practice Back Click for trig ratios

  20. You try! Solve for x. 39˚ 16 x Back Click for trig ratios Click for answer

  21. x = 10.1 answer: Back Click for trig ratios Click for another

  22. You try! Solve for x. 10 31˚ x Back Click for trig ratios Click for answer

  23. x = 8.6 answer: Back Click for trig ratios Click for another

  24. You try! Solve for x. x 44˚ 23 Back Click for trig ratios Click for answer

  25. x = 22.2 answer: Back Click for trig ratios Click for more

  26. For more information… @Home Tutor – Right Triangle Trig YourTeacher – Solving for sidesusingTrigvideo Right Triangle Calculator and Solver This Stand AloneInstructional Resource wascreatedusing PowerPoint. All sounds arealsofrom PowerPoint. Information, definitions, and exampleswereadaptedfrom in McDougall Littell’sMathematics 2 textbook. Click to start over

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