8.3 tangent ratio - poudre school districtstaffweb.psdschools.org/kemotich/mrs_motichka... · 8.3...
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![Page 1: 8.3 Tangent Ratio - Poudre School Districtstaffweb.psdschools.org/kemotich/Mrs_Motichka... · 8.3 Tangent Ratio 10 March 04, 2010 Feb 249:53 PM The inverse of the tangent ratio If](https://reader034.vdocuments.site/reader034/viewer/2022042806/5f6be1c0db64935a246c6988/html5/thumbnails/1.jpg)
8.3 Tangent Ratio
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March 04, 2010
Feb 238:28 AM
8.3: Tangent Ratio
Objective: Use the tangent ratio to determine side lengths in right triangles.
![Page 2: 8.3 Tangent Ratio - Poudre School Districtstaffweb.psdschools.org/kemotich/Mrs_Motichka... · 8.3 Tangent Ratio 10 March 04, 2010 Feb 249:53 PM The inverse of the tangent ratio If](https://reader034.vdocuments.site/reader034/viewer/2022042806/5f6be1c0db64935a246c6988/html5/thumbnails/2.jpg)
8.3 Tangent Ratio
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March 04, 2010
Feb 2411:37 AM
For each triangle identify the length of the hypotenuse, the length of the side opposite angle B, and the length of the side adjacent to angle B.
![Page 3: 8.3 Tangent Ratio - Poudre School Districtstaffweb.psdschools.org/kemotich/Mrs_Motichka... · 8.3 Tangent Ratio 10 March 04, 2010 Feb 249:53 PM The inverse of the tangent ratio If](https://reader034.vdocuments.site/reader034/viewer/2022042806/5f6be1c0db64935a246c6988/html5/thumbnails/3.jpg)
8.3 Tangent Ratio
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Feb 2411:47 AM
36.87o
53.13o
6
8
10
36.87o
53.13o
9
12
15
36.87o
53.13o
UVTV
=
TVUV
=
UVTV
=
TVUV
=
UVTV
=
TVUV
=
![Page 4: 8.3 Tangent Ratio - Poudre School Districtstaffweb.psdschools.org/kemotich/Mrs_Motichka... · 8.3 Tangent Ratio 10 March 04, 2010 Feb 249:53 PM The inverse of the tangent ratio If](https://reader034.vdocuments.site/reader034/viewer/2022042806/5f6be1c0db64935a246c6988/html5/thumbnails/4.jpg)
8.3 Tangent Ratio
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March 04, 2010
Feb 2411:49 AM
tan ( ) = A
B
A C
Leg opposite A
Leg adjacent to A
For each pair of complementary angles, and , there is a family of similar right triangles. In each such family, the tangent ratio is constant no matter the size of ABC.
A B
tan ( ) = B
What is the tangent of B in the above diagram?
![Page 5: 8.3 Tangent Ratio - Poudre School Districtstaffweb.psdschools.org/kemotich/Mrs_Motichka... · 8.3 Tangent Ratio 10 March 04, 2010 Feb 249:53 PM The inverse of the tangent ratio If](https://reader034.vdocuments.site/reader034/viewer/2022042806/5f6be1c0db64935a246c6988/html5/thumbnails/5.jpg)
8.3 Tangent Ratio
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March 04, 2010
Feb 247:24 PM
Write the tangent ratio for T and U.
Step 1: Identify the opposite and adjacent sides from the angle.
Step 2: Write the tangent ratio.
![Page 6: 8.3 Tangent Ratio - Poudre School Districtstaffweb.psdschools.org/kemotich/Mrs_Motichka... · 8.3 Tangent Ratio 10 March 04, 2010 Feb 249:53 PM The inverse of the tangent ratio If](https://reader034.vdocuments.site/reader034/viewer/2022042806/5f6be1c0db64935a246c6988/html5/thumbnails/6.jpg)
8.3 Tangent Ratio
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Feb 247:42 PM
We can also use the tangent ratio to find the side lengths of right triangles.
Ex) Find the value of w to the nearest tenth.
Step 1: Identify the opposite and adjacent sides from the angle.
Step 2: Write the tangent ratio and solve for w.
Step 3: Get your handydandy calculator and plug it in.
![Page 7: 8.3 Tangent Ratio - Poudre School Districtstaffweb.psdschools.org/kemotich/Mrs_Motichka... · 8.3 Tangent Ratio 10 March 04, 2010 Feb 249:53 PM The inverse of the tangent ratio If](https://reader034.vdocuments.site/reader034/viewer/2022042806/5f6be1c0db64935a246c6988/html5/thumbnails/7.jpg)
8.3 Tangent Ratio
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March 04, 2010
Feb 247:42 PM
We can also use the tangent ratio to find the side lengths of right triangles.
Ex) Find the value of w to the nearest tenth.
Step 1: Identify the opposite and adjacent sides from the angle.
Step 2: Write the tangent ratio and solve for w.
Step 3: Get your handydandy calculator and plug it in.
![Page 8: 8.3 Tangent Ratio - Poudre School Districtstaffweb.psdschools.org/kemotich/Mrs_Motichka... · 8.3 Tangent Ratio 10 March 04, 2010 Feb 249:53 PM The inverse of the tangent ratio If](https://reader034.vdocuments.site/reader034/viewer/2022042806/5f6be1c0db64935a246c6988/html5/thumbnails/8.jpg)
8.3 Tangent Ratio
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March 04, 2010
Feb 247:49 PM
People actually use this stuff!!!!(Can you believe it?)
The tangent ratio can be used to measure distances that would be difficult to measure directly.
For instance: The distance from the earth to the moon and any other celestial body we can see.
![Page 9: 8.3 Tangent Ratio - Poudre School Districtstaffweb.psdschools.org/kemotich/Mrs_Motichka... · 8.3 Tangent Ratio 10 March 04, 2010 Feb 249:53 PM The inverse of the tangent ratio If](https://reader034.vdocuments.site/reader034/viewer/2022042806/5f6be1c0db64935a246c6988/html5/thumbnails/9.jpg)
8.3 Tangent Ratio
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Feb 248:58 PM
Let us try it: Find the distance from the earth to the moon.drawing not to scale
0.955o
3,950 mi
x
Average distance from the earth to the moon: 238,855 mi
![Page 10: 8.3 Tangent Ratio - Poudre School Districtstaffweb.psdschools.org/kemotich/Mrs_Motichka... · 8.3 Tangent Ratio 10 March 04, 2010 Feb 249:53 PM The inverse of the tangent ratio If](https://reader034.vdocuments.site/reader034/viewer/2022042806/5f6be1c0db64935a246c6988/html5/thumbnails/10.jpg)
8.3 Tangent Ratio
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March 04, 2010
Feb 249:53 PM
The inverse of the tangent ratioIf we know the tangent ratio, we can also use the inverse of tangent to find the angle measure.
Ex) Find the value of x to the nearest degree.
Step 1: Identify the opposite and adjacent sides from the angle.
Step 2: Write the tangent ratio.
Step 3: Get your handydandy calculator and plug it in.
![Page 11: 8.3 Tangent Ratio - Poudre School Districtstaffweb.psdschools.org/kemotich/Mrs_Motichka... · 8.3 Tangent Ratio 10 March 04, 2010 Feb 249:53 PM The inverse of the tangent ratio If](https://reader034.vdocuments.site/reader034/viewer/2022042806/5f6be1c0db64935a246c6988/html5/thumbnails/11.jpg)
8.3 Tangent Ratio
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March 04, 2010
Feb 249:53 PM
The inverse of the tangent ratioIf we know the tangent ratio, we can also use the inverse of tangent to find the angle measure.
Ex) Find the value of x to the nearest degree.
Step 1: Identify the opposite and adjacent sides from the angle.
Step 2: Write the tangent ratio.
Step 3: Get your handydandy calculator and plug it in.
![Page 12: 8.3 Tangent Ratio - Poudre School Districtstaffweb.psdschools.org/kemotich/Mrs_Motichka... · 8.3 Tangent Ratio 10 March 04, 2010 Feb 249:53 PM The inverse of the tangent ratio If](https://reader034.vdocuments.site/reader034/viewer/2022042806/5f6be1c0db64935a246c6988/html5/thumbnails/12.jpg)
8.3 Tangent Ratio
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Feb 2410:09 PM
Homework
Pg. 434# 1 9 odd, 11 15 odd,
22 and 31