2. Right Triangle Triginometry A Stand-Alone Instructional Resource Created by Lindsay Sanders

3. 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 hypotenuse adjacent opposite To learn more, please watch this video

4. Trigonometric Ratios SineCosine Tangent Click on the trigonometric ratios below to learn more.

5. 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 length of hypotenuse AB Sin A = = A B C opposite hypotenuse Click for example Click for trig ratios length of leg opposite  A BC

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

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

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

9. A trigonometric ratio for acute angles that involve the length of the adjacent side and the hypotenuse of a right triangle, abbreviated Cos length of hypotenuseAB Cos A = = A B C adjacent hypotenuse Click for example Click for trig ratios length of leg adjacent  A AC

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

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

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

13. A trigonometric ratio for acute angles that involve the length of the opposite side and the adjacent side of a right triangle, abbreviated Tan length of leg adjacentAC Tan A = = A B C adjacent Click for example opposite Click for trig ratios length of leg opposite  A BC

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

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

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

17. 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! 52 x 42 ˚ Click for trig ratios Click for example

18. Example 4 Solve for x. 52 x 42 ˚ 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. Sin 42 ˚ = x 52 Multiply both side by 52 · 5252 · Put 52 · sin 42 in calculator 34.8 = x Click for practice Click for trig ratios Back

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

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

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

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

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

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

25. 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