7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine...
-
Upload
luke-lawrence -
Category
Documents
-
view
222 -
download
0
Transcript of 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine...
![Page 1: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/1.jpg)
7.6
Warm UpWarm Up
Lesson QuizLesson Quiz
Lesson PresentationLesson Presentation
Apply the Sine and Cosine Ratios
![Page 2: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/2.jpg)
7.6 Warm-Up
2. Name the leg opposite X.
1. Name the hypotenuse.
Use this diagram for Exercises 1-4.
ANSWER YZ
ANSWER XZ
![Page 3: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/3.jpg)
7.6 Warm-Up
Use this diagram for Exercises 1-4.
ANSWER 14.78
3. Name the leg adjacent to X.
4. If XY = 17 and m X = 41 , find AC.
ANSWER XY
![Page 4: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/4.jpg)
7.6 Example 1
Find sin S and sin R. Write each answer as a fraction and as a decimal rounded to four places.
SOLUTION
sin S = opp. Shyp
= RTSR = 63
65 0.9692
sin R = opp. Rhyp
= STSR = 16
65 0.2462
![Page 5: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/5.jpg)
7.6 Guided Practice
Find sin X and sin Y. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary.
ANSWER 817
0.4706, or 1517
0.8824 or
1.
![Page 6: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/6.jpg)
7.6 Guided Practice
Find sin X and sin Y. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary.
ANSWER 35
0.6, or 45
0.8 or
2.
![Page 7: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/7.jpg)
7.6 Example 2
Find cos U and cos W. Write each answer as a fraction and as a decimal.
cos U = adj. to U hyp
= UVUW = 18
30 = 0.6000
cos W = adj. to W hyp
= WVUW = 24
30
SOLUTION
= 35
= 45 = 0.8000
![Page 8: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/8.jpg)
7.6 Example 3
DOG RUN You want to string cable to make a dog run from two corners of a building, as shown in the diagram. Write and solve a proportion using a trigonometric ratio to approximate the length of cable you will need.
![Page 9: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/9.jpg)
7.6 Example 3
SOLUTION
sin 35° =opp. hyp.
Write ratio for sine of 35o.
sin 35° = 11x
Substitute.
x sin 35° = 11 Multiply each side by x.
x = 11 sin 35°
Divide each side by sin 35o.
x 11 0.5736
Use a calculator to find sin 35o.
x 19.2 Simplify.
You will need a little more than 19 feet of cable.
![Page 10: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/10.jpg)
7.6 Guided Practice
In Exercises 3 and 4, find cos R and cos S. Write each answer as a decimal. Round to four decimal places, if necessary.
3.
ANSWER 0.6, 0.8
![Page 11: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/11.jpg)
7.6 Guided Practice
In Exercises 3 and 4, find cos R and cos S. Write each answer as a decimal. Round to four decimal places, if necessary.
4.
ANSWER 0.8824, 0.4706
![Page 12: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/12.jpg)
7.6 Guided Practice
In Example 3, use the cosine ratio to find the length of the other leg of the triangle formed.
5.
ANSWER about 15.7 ft
![Page 13: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/13.jpg)
7.6 Example 4
SKIING You are skiing on a mountain with an altitude of 1200 meters. The angle of depression is 21°. About how far do you ski down the mountain?
![Page 14: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/14.jpg)
7.6 Example 4
SOLUTION
Write ratio for sine of 21o.
Substitute.
x sin 21° = 1200 Multiply each side by x.
x = 1200 sin 21°
Divide each side by sin 21o
x 1200 0.3584
Use a calculator to find sin 21o
x 3348.2 Simplify.
sin 21°opp. hyp.=
sin 21° 1200
x=
You ski about 3348 meters down the mountain.
![Page 15: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/15.jpg)
7.6 Guided Practice
6. WHAT IF? Suppose the angle of depression in Example 4 is 28°. About how far would you ski?
ANSWER about 2556 m
![Page 16: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/16.jpg)
7.6 Example 5
SKATEBOARD RAMP You want to build a skateboard ramp with a length of 14 feet and an angle of elevation of 26°. You need to find the height and length of the base of the ramp.
![Page 17: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/17.jpg)
7.6 Example 5
SOLUTION
sin 26° =opp. hyp. Write ratio for sine of 26o.
sin 26° x
=14 Substitute.
14 sin 26° = x Multiply each side by 14.
6.1 x Use a calculator to simplify.
STEP 1 Find the height.
The height is about 6.1 feet.
![Page 18: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/18.jpg)
7.6 Example 5
cos 26° =adj. hyp. Write ratio for cosine of 26o.
cos 26° y
=14 Substitute.
14 cos 26° = y Multiply each side by 14.
12.6 y Use a calculator to simplify.
STEP 2 Find the length of the base.
The length of the base is about 12.6 feet.
![Page 19: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/19.jpg)
7.6 Example 6
Use a special right triangle to find the sine and cosine of a 60o angle.
SOLUTION
sin 60° =opp. hyp.
=3
20.08660
cos 60° =adj. hyp.
=21
0.5000=
Use the 30° - 60° - 90° Triangle Theorem to draw a right triangle with side lengths of 1, , and 2. Then set up sine and cosine ratios for the 60° angle.
3
![Page 20: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/20.jpg)
7.6 Guided Practice
7. WHAT IF? In Example 5, suppose the angle of elevation is 35°. What is the new height and base length of the ramp?
ANSWER about 8 feet, about 11.5 ft
8. Use a special right triangle to find the sine and cosine of a 30° angle.
ANSWER 1 2
,23
![Page 21: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/21.jpg)
7.6 Lesson Quiz
Use this diagram for Exercises 1- 3.
1. If x = , y = 4 and z = , find sin X, sin Y, cos X and cos Y.
5 4 6 4
ANSWER sin X = 306
0.9129, sin Y = 0.4082,66
cos Y = 306
0.9129cos X = 0.4082,66
![Page 22: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/22.jpg)
7.6 Lesson Quiz
Use this diagram for Exercises 1- 3.
ANSWER 38.6
2. If y = 10 and m Y = 15° , find z to the nearest tenth.
![Page 23: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/23.jpg)
7.6 Lesson Quiz
Use this diagram for Exercises 1- 3.
ANSWER 1.3
3. If z = 12 and m X = 84° , find y to the nearest tenth.
![Page 24: 7.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Sine and Cosine Ratios.](https://reader036.fdocuments.in/reader036/viewer/2022082517/56649f295503460f94c42617/html5/thumbnails/24.jpg)
7.6 Lesson Quiz
ANSWER 14.6 ft
4. A lamppost is 11 feet tall. If the angle of elevation of the sun is 49° , how far is the top of the lamppost from the tip of its shadow?