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![Page 1: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/1.jpg)
Trigonometry-6
Finding Angles in Triangles
![Page 2: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/2.jpg)
Trigonometry
Find angles using a calculator
Examples to find sin, cos and tan ratios of angles
Examples to find angles
![Page 3: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/3.jpg)
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 .
![Page 4: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/4.jpg)
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
![Page 5: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/5.jpg)
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 .
![Page 6: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/6.jpg)
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.
![Page 7: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/7.jpg)
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.
![Page 8: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/8.jpg)
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.
![Page 9: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/9.jpg)
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
![Page 10: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/10.jpg)
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
![Page 11: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/11.jpg)
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
![Page 12: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/12.jpg)
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
![Page 13: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/13.jpg)
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
![Page 14: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/14.jpg)
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
![Page 15: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/15.jpg)
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
![Page 16: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/16.jpg)
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 =
![Page 17: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/17.jpg)
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 =
![Page 18: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/18.jpg)
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 =
![Page 19: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/19.jpg)
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 =
![Page 20: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/20.jpg)
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 =
![Page 21: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/21.jpg)
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 =
![Page 22: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/22.jpg)
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
![Page 23: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/23.jpg)
Well Done!
![Page 24: Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649db05503460f94a9e443/html5/thumbnails/24.jpg)
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