1. Trigonometry-6 Finding Angles in Triangles

2. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to find angles

3. Finding Ratios  What you have learned up to now is, for a given angle, to find the ratios of sides.  So, for angle  we have: Tan  = P Q R  opposite adjacent Hypotenuse Opposite Adjacent Cos  = adjacent hypotenuse Sin  = opposite hypotenuse If we know two sides we can find the trig ratio. Now we will learn how to find the angle .

4. To Find sin, cos or tan of an angle  Your scientific calculator has sin, cos and tan keys.  To find the sin, cos or tan of an angle, enter the angle and then press the relevant key. Find sin 30  :Enter 30, then press the sin key Answer = 0.5

5. Finding Angles  Your scientific calculator has sin -1, cos -1 and tan -1 keys.  These are labels above the sin, cos and tan keys.  To activate them press the Inverse (INV) or Shift or Alternate (ALT) key, then press the sin, cos or tan key.  You will have to find which key to press on your calculator. sin -1  is called arcsin . cos -1  is called arccos . tan -1  is called arctan .

6. To Find an Angle  Find: sin 30   Find angle X if: sin X = 0.5 Answer: X = 30  Enter 30, then press the sin key. Answer: sin 30  = 0.5 Enter 0.5, then press the INV or ALT key, then press the sin key.

7. To Find an Angle  Find: cos 30   Find angle  if: cos  = 0.866 Answer:  = 30  Enter 30, then press the cos key. Answer: cos 30  = 0.866 Enter 0.866, then press the INV or ALT key, then press the cos key.

8. To Find an Angle  Find: tan 45   Find angle X if: tan X = 1 Answer: X = 45  Enter 45, then press the tan key. Answer: tan 45  = 1 Enter 1, then press the INV or ALT key, then press the tan key.

9.  Complete the table by clicking on what you think are the right answers. Work from the top down. Fill in the Answers 0.4452 Find Sin 66  Cos 34  Tan 24  Sin 21  Cos 65  Tan 59  AnswerPossible Answers 0.7193 0.9135 0.6745 0.3583 0.5150 0.8290 0.4226 0.5591 1.6642 1 2 3 4 5 6

10.  Complete the table by clicking on what you think are the right answers. Work from the top down. Fill in the Answers 0.4452 Find Sin 66  Cos 34  Tan 24  Sin 21  Cos 65  Tan 59  AnswerPossible Answers 0.7193 0.9135 0.6745 0.3583 0.5150 0.8290 0.4226 0.5591 1.6642 0.9135 1 2 3 4 5 6

11.  Complete the table by clicking on what you think are the right answers. Work from the top down. Fill in the Answers 0.4452 Find Sin 66  Cos 34  Tan 24  Sin 21  Cos 65  Tan 59  AnswerPossible Answers 0.7193 0.9135 0.6745 0.3583 0.5150 0.8290 0.4226 0.5591 1.6642 0.9135 0.8290 1 2 3 4 5 6

12.  Complete the table by clicking on what you think are the right answers. Work from the top down. Fill in the Answers 0.4452 Find Sin 66  Cos 34  Tan 24  Sin 21  Cos 65  Tan 59  AnswerPossible Answers 0.7193 0.9135 0.6745 0.3583 0.5150 0.8290 0.4226 0.5591 1.6642 0.9135 0.8290 0.4452 1 2 3 4 5 6

13.  Complete the table by clicking on what you think are the right answers. Work from the top down. Fill in the Answers 0.4452 Find Sin 66  Cos 34  Tan 24  Sin 21  Cos 65  Tan 59  AnswerPossible Answers 0.7193 0.9135 0.6745 0.3583 0.5150 0.8290 0.4226 0.5591 1.6642 0.9135 0.8290 0.4452 0.3583 1 2 3 4 5 6

14.  Complete the table by clicking on what you think are the right answers. Work from the top down. Fill in the Answers 0.4452 Find Sin 66  Cos 34  Tan 24  Sin 21  Cos 65  Tan 59  AnswerPossible Answers 0.7193 0.9135 0.6745 0.3583 0.5150 0.8290 0.4226 0.5591 1.6642 0.9135 0.8290 0.4452 0.3583 0.4226 1 2 3 4 5 6

15.  Complete the table by clicking on what you think are the right answers. Work from the top down. Fill in the Answers 0.4452 Find Sin 66  Cos 34  Tan 24  Sin 21  Cos 65  Tan 59  AnswerPossible Answers 0.7193 0.9135 0.6745 0.3583 0.5150 0.8290 0.4226 0.5591 1.6642 1 2 3 4 5 6 0.9135 0.8290 0.4452 0.3583 0.4226 1.6642

16.  Complete the table by clicking on what you think are the right answers for X. Work from the top down. Find the Angles X = 54  Find X Sin X  = 0.72 Cos X  = 0.39 Tan X  = 0.177 Sin X  = 0.293 Cos X  = 0.742 Tan X  = 1.33 AnswerPossible Answers X = 46  X = 71  X = 67  X = 19  X = 17  X = 49  X = 10  X = 42  X = 53  X = 31  1 2 3 4 5 6 X =

17.  Complete the table by clicking on what you think are the right answers for X or . Work from the top down. Find the Angles X = 54  Find X Sin X  = 0.72 Cos X  = 0.39 Tan X  = 0.177 Sin X  = 0.293 Cos X  = 0.742 Tan X  = 1.33 AnswerPossible Answers X = 46  X = 71  X = 67  X = 19  X = 17  X = 49  X = 10  X = 42  X = 53  X = 31  1 2 3 4 5 6 X = 46  X =

18.  Complete the table by clicking on what you think are the right answers for X or . Work from the top down. Find the Angles X = 54  Find X Sin X  = 0.72 Cos X  = 0.39 Tan X  = 0.177 Sin X  = 0.293 Cos X  = 0.742 Tan X  = 1.33 AnswerPossible Answers X = 46  X = 71  X = 67  X = 19  X = 17  X = 49  X = 10  X = 42  X = 53  X = 31  1 2 3 4 5 6 X = 46  X = 67  X =

19.  Complete the table by clicking on what you think are the right answers for X or . Work from the top down. Find the Angles X = 54  Find X Sin X  = 0.72 Cos X  = 0.39 Tan X  = 0.177 Sin X  = 0.293 Cos X  = 0.742 Tan X  = 1.33 AnswerPossible Answers X = 46  X = 71  X = 67  X = 19  X = 17  X = 49  X = 10  X = 42  X = 53  X = 31  1 2 3 4 5 6 X = 46  X = 67  X = 10  X =

20.  Complete the table by clicking on what you think are the right answers for X or . Work from the top down. Find the Angles X = 54  Find X Sin X  = 0.72 Cos X  = 0.39 Tan X  = 0.177 Sin X  = 0.293 Cos X  = 0.742 Tan X  = 1.33 AnswerPossible Answers X = 46  X = 71  X = 67  X = 19  X = 17  X = 49  X = 10  X = 42  X = 53  X = 31  1 2 3 4 5 6 X = 46  X = 67  X = 10  X = 17  X =

21.  Complete the table by clicking on what you think are the right answers for X or . Work from the top down. Find the Angles X = 54  Find X Sin X  = 0.72 Cos X  = 0.39 Tan X  = 0.177 Sin X  = 0.293 Cos X  = 0.742 Tan X  = 1.33 AnswerPossible Answers X = 46  X = 71  X = 67  X = 19  X = 17  X = 49  X = 10  X = 42  X = 53  X = 31  1 2 3 4 5 6 X = 46  X = 67  X = 10  X = 17  X = 42  X =

22.  Complete the table by clicking on what you think are the right answers for X or . Work from the top down. Find the Angles X = 54  Find X Sin X  = 0.72 Cos X  = 0.39 Tan X  = 0.177 Sin X  = 0.293 Cos X  = 0.742 Tan X  = 1.33 AnswerPossible Answers X = 46  X = 71  X = 67  X = 19  X = 17  X = 49  X = 10  X = 42  X = 53  X = 31  1 2 3 4 5 6 X = 46  X = 67  X = 10  X = 17  X = 42  X = 53 

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