L1 Terms Ratios Find Missing Side
-
Upload
kliegey524 -
Category
Technology
-
view
3.875 -
download
1
description
Transcript of L1 Terms Ratios Find Missing Side
![Page 1: L1 Terms Ratios Find Missing Side](https://reader033.fdocuments.net/reader033/viewer/2022042714/5562774ad8b42ad1688b4759/html5/thumbnails/1.jpg)
![Page 2: L1 Terms Ratios Find Missing Side](https://reader033.fdocuments.net/reader033/viewer/2022042714/5562774ad8b42ad1688b4759/html5/thumbnails/2.jpg)
Find the three basic trigonometric ratios in a right triangle.Use trigonometric ratios to find missing lengths.
Objectives
![Page 3: L1 Terms Ratios Find Missing Side](https://reader033.fdocuments.net/reader033/viewer/2022042714/5562774ad8b42ad1688b4759/html5/thumbnails/3.jpg)
trigonometric ratiossinecosinetangent
Vocabulary
![Page 4: L1 Terms Ratios Find Missing Side](https://reader033.fdocuments.net/reader033/viewer/2022042714/5562774ad8b42ad1688b4759/html5/thumbnails/4.jpg)
A trigonometric ratio is a ratio of the lengths of two sides in a right triangle. Three basic trigonometric ratios are sine, cosine, and tangent, abbreviated sin, cos, and tan, respectively.
![Page 5: L1 Terms Ratios Find Missing Side](https://reader033.fdocuments.net/reader033/viewer/2022042714/5562774ad8b42ad1688b4759/html5/thumbnails/5.jpg)
![Page 6: L1 Terms Ratios Find Missing Side](https://reader033.fdocuments.net/reader033/viewer/2022042714/5562774ad8b42ad1688b4759/html5/thumbnails/6.jpg)
Confused?
Here’s an acronym to help you remember the ratios
Sine = Opposite divided by Hypotenuse
Cosine = Adjacent divided by Hypotenuse
Tangent = Opposite divided by Adjacent
SOH CAH TOA
![Page 7: L1 Terms Ratios Find Missing Side](https://reader033.fdocuments.net/reader033/viewer/2022042714/5562774ad8b42ad1688b4759/html5/thumbnails/7.jpg)
Example 1: Finding the Value of a Trigonometric Ratio
Find sin A, cos A and tan A.
A
BC
17
15
8
Sin ASin A
Cos A
Cos A
Tan ATan A
![Page 8: L1 Terms Ratios Find Missing Side](https://reader033.fdocuments.net/reader033/viewer/2022042714/5562774ad8b42ad1688b4759/html5/thumbnails/8.jpg)
COMMON ERRORALERT
Students tend to make simple mistakes bymislabeling the adjacent and opposite sides
To overcome this mistake first determine theHypotenuse (should be easy right?)
Then determine the opposite side (across fromthe angle referred to.)
The remaining side is the adjacent side.
![Page 9: L1 Terms Ratios Find Missing Side](https://reader033.fdocuments.net/reader033/viewer/2022042714/5562774ad8b42ad1688b4759/html5/thumbnails/9.jpg)
Find each trigonometric ratio to the nearest thousandth.
Check It Out! Example 2
Sin BSin B =
Cos B
Cos B =
Tan BTan B =
![Page 10: L1 Terms Ratios Find Missing Side](https://reader033.fdocuments.net/reader033/viewer/2022042714/5562774ad8b42ad1688b4759/html5/thumbnails/10.jpg)
To find trigonometric ratios on a graphing calculator, press and then the value of the degree. Be sure your calculator is in degrees.
Helpful Hint
![Page 11: L1 Terms Ratios Find Missing Side](https://reader033.fdocuments.net/reader033/viewer/2022042714/5562774ad8b42ad1688b4759/html5/thumbnails/11.jpg)
Example 3: Application
A ladder is leaning against a wall. The base of the ladder makes a 60° angle with the ground. The base of the ladder is 17 feet from the wall. What is the length of the ladder?Draw a diagram to model the problem.
17 ft.60°
wallladder
A
A B
Cross multiply.
cos A =
The ladder is 34 feet long.
= 34
![Page 12: L1 Terms Ratios Find Missing Side](https://reader033.fdocuments.net/reader033/viewer/2022042714/5562774ad8b42ad1688b4759/html5/thumbnails/12.jpg)
Check It Out! Example 4
Construction A 14-foot ladder is leaning against a building. The ladder makes a 70° angle with the ground. How far is the base of the ladder from the building? Round your answer to the nearest tenth of a foot.
Draw a diagram to model the problem.
cos A =x ft.
70°
wallladder(14 ft)
A B
cos 70° =
adjacent = 14(cos 70°) 4.8
The ladder’s base is about 4.8 feet from the building.
Multiply both sides by 14.
![Page 13: L1 Terms Ratios Find Missing Side](https://reader033.fdocuments.net/reader033/viewer/2022042714/5562774ad8b42ad1688b4759/html5/thumbnails/13.jpg)
A
C B
2524
7
Take out a piece of paper.Write your name at the top.
Find each trigonometric ratio to the nearest thousandth.
1.Sin B2.Cos B3.Tan B