Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs....
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Transcript of Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs....
![Page 1: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/1.jpg)
Original Power PointFrom
mackinac.eup.k12.mi.us/cms/lib/Mackinac Island Public School
Author:Mrs. Bennett
![Page 2: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/2.jpg)
The Trigonometric Functions we will be
looking at
SINE
COSINE
TANGENT
![Page 3: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/3.jpg)
Old Hippie
Old Hippie
SomeOldHippieCameAHoppin’ThroughOurApartment
![Page 4: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/4.jpg)
SOHCAHTOA
Old Hippie
Old Hippie
SinOppHypCosAdjHypTanOppAdj
![Page 5: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/5.jpg)
Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth.
5520 m
x
20
55tanx
m 6.28x
x55tan20tan 20 55 )
Shrink yourself down and stand where the angle is.
Now, figure out which trig ratio you have and set up the problem.
![Page 6: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/6.jpg)
Ex: 2 Find the missing side. Round to the nearest tenth.
72
80 ft
x
x
8072tan
ft 26x
8072tan x
72tan
80x
tan 80 72 = ( ) )Shrink yourself down and stand where the angle is.Now, figure out which trig ratio you have and set up the problem.
![Page 7: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/7.jpg)
New Version…
![Page 8: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/8.jpg)
The Trigonometric Ratios
SINECOSINETANGENT
The trigonometric ratios can be used to find a missing side of a right triangle or an
angle.
I smell a hippie!
![Page 9: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/9.jpg)
SOH CAH TOA
Old Hippie
Old Hippie
SinOppHypCosAdjHypTanOppAdj
![Page 10: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/10.jpg)
Some
Old
Hippie
Came
AHoppin’
Through
OurApartment
Maybe this will help…
Old Hippie
Old Hippie
![Page 11: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/11.jpg)
I knew I smelled a hippie!!
Now, how do we use this trig stuff?
![Page 12: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/12.jpg)
Step 1Figure out which ratio to use.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
![Page 13: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/13.jpg)
Step 1Figure out which ratio to use.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Label the sides of the triangle using the reference angle as the starting point.
Draw an arrow straight from the reference angle, that is the opposite Leg
Opposite Leg
![Page 14: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/14.jpg)
Step 1Figure out which ratio to use.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Opposite the right angle is the hypotenuse.
Opposite Leg
Hypotenuse
![Page 15: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/15.jpg)
Step 1Figure out which ratio to use.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Lastly, label the remaining leg the Adjacent Leg
Opposite Leg
Hypotenuse
Adjacent Leg
![Page 16: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/16.jpg)
Step 1Figure out which ratio to use.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
The triangle gives you the ADJACENT LEG and is looking for the OPPOSITE LEG.
Opposite Leg
Hypotenuse
Adjacent Leg
![Page 17: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/17.jpg)
Step 1Figure out which ratio to use.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
TANGENT uses the OPPOSITE and ADJACENT leg
Opposite Leg
Hypotenuse
Adjacent Leg
![Page 18: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/18.jpg)
Step 2Using the Trig ratio.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Plug in the information present.
Opposite Leg
Hypotenuse
Adjacent Leg
Tan(55)=
![Page 19: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/19.jpg)
Step 2Using the Trig ratio.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Insert a “1” under the Tan(55).
Opposite Leg
Hypotenuse
Adjacent Leg
=
![Page 20: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/20.jpg)
Step 2Using the Trig ratio.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Cross multiply
Opposite Leg
Hypotenuse
Adjacent Leg
=
![Page 21: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/21.jpg)
Step 2Using the Trig ratio.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Cross multiply
Opposite Leg
Hypotenuse
Adjacent Leg
20 ∙𝑇𝑎𝑛 (55 )=𝑥
![Page 22: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/22.jpg)
Step 2Using the Trig ratio.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Enter that into your calculator..
20 ∙𝑇𝑎𝑛 (55 )=𝑥
Adjacent Leg
Opposite Leg
Hypotenuse
![Page 23: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/23.jpg)
Step 2Using the Trig ratio.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
The calculator does all of the hard work!
2 8.56=𝑥
![Page 24: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/24.jpg)
Step 2Using the Trig ratio.
5520 m
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
That is your answer.
28.56 m
![Page 25: Original Power Point From mackinac.eup.k12.mi.us/cms/lib/ Mackinac Island Public School Author: Mrs. Bennett.](https://reader035.fdocuments.us/reader035/viewer/2022062423/5697bfa71a28abf838c9901e/html5/thumbnails/25.jpg)
Step 2Using the Trig ratio.
5520 m
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Done!
28.56 m
They all work the same man! It works every time!!