Trigonometry-6

Finding Angles in Triangles

Trigonometry

Find angles using a calculator

Examples to find sin, cos and tan ratios of angles

Examples to find angles

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

Opp

osite

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 .

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

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 .

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.

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.

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.

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

Answer

Possible 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

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

Answer

Possible Answers

0.7193

0.9135

0.6745

0.3583

0.5150

0.8290

0.4226

0.5591

1.6642

0.91351

2

3

4

5

6

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

Answer

Possible 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

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

Answer

Possible 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

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

Answer

Possible 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

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

Answer

Possible 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

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

Answer

Possible 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

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

Answer

Possible 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 =

X =

X =

X =

X =

X =

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

Answer

Possible 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 =

X =

X =

X =

X =

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

Answer

Possible 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 =

X =

X =

X =

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

Answer

Possible 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 =

X =

X =

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

Answer

Possible 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 =

X =

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

Answer

Possible 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 =

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

Answer

Possible 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

Well Done!

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