Download Law of Sines and Law of Cosines

e x p l o r at i o n
of Sines and
8-5 Law
Law of Cosines
You can use certain trigonometric relationships to solve any
triangle. To do so, you will need to find trigonometric ratios for
angle measures up to 180˚.
1. Use your calculator to find the trigonometric ratios in the
table. Round to the nearest hundredth.
90˚
110˚
139˚
164˚
174˚
Sine
Cosine
Tangent
2. What happened when you used your calculator to find
tan 90˚? Why do you think this happened?
3. For angles between 90˚ and 180˚, how is the sine ratio
different from the cosine and tangent ratios?
4. Which trigonometric ratio increases as the angle measures
increase from 90˚ to 180˚?
THINK AND DISCUSS
5. Discuss whether you think there is an angle measure
between 90˚ and 180˚ whose sine and cosine ratios are equal.
6. Explain how you can use your completed table to estimate
the measure of an angle if you know that its cosine is 0.98.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
53
Holt Geometry
e x p l o r at i o n
of Sines and
8-5 Law
Law of Cosines
You can use certain trigonometric relationships to solve any
triangle. To do so, you will need to find trigonometric ratios for
angle measures up to 180˚.
1. Use your calculator to find the trigonometric ratios in the
table. Round to the nearest hundredth.
Sine
Cosine
Tangent
90˚
110˚
139˚
164˚
174˚
1
0.94
0.66
0.28
0.10
0
0.34
0.75
0.96
0.99
—
2.75
0.87
0.29
0.11
2. What happened when you used your calculator to find
tan 90˚? Why do you think this happened?
Error message; the tangent ratio is not defined for 90˚.
3. For angles between 90˚ and 180˚, how is the sine ratio
different from the cosine and tangent ratios?
The sine is positive; the cosine and tangent are negative.
4. Which trigonometric ratio increases as the angle measures
increase from 90˚ to 180˚? tangent
THINK AND DISCUSS
5. Discuss whether you think there is an angle measure
between 90˚ and 180˚ whose sine and cosine ratios are equal.
No; for angles between 90˚ and 180˚, the sine is positive, and the cosine is negative.
So the two ratios cannot be equal.
6. Explain how you can use your completed table to estimate
the measure of an angle if you know that its cosine is 0.98.
Based on the table, the angle must be between 164˚ and 174˚.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
53
Holt Geometry