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mackinac.eup.k12.mi.us/cms/lib/Mackinac Island Public School
Author:Mrs. Bennett
The Trigonometric Functions we will be
looking at
SINE
COSINE
TANGENT
Old Hippie
Old Hippie
SomeOldHippieCameAHoppin’ThroughOurApartment
SOHCAHTOA
Old Hippie
Old Hippie
SinOppHypCosAdjHypTanOppAdj
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.
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.
New Version…
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!
SOH CAH TOA
Old Hippie
Old Hippie
SinOppHypCosAdjHypTanOppAdj
Some
Old
Hippie
Came
AHoppin’
Through
OurApartment
Maybe this will help…
Old Hippie
Old Hippie
I knew I smelled a hippie!!
Now, how do we use this trig stuff?
Step 1Figure out which ratio to use.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
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
Step 1Figure out which ratio to use.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Opposite the right angle is the hypotenuse.
Opposite Leg
Hypotenuse
Step 1Figure out which ratio to use.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Lastly, label the remaining leg the Adjacent Leg
Opposite Leg
Hypotenuse
Adjacent Leg
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
Step 1Figure out which ratio to use.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
TANGENT uses the OPPOSITE and ADJACENT leg
Opposite Leg
Hypotenuse
Adjacent Leg
Step 2Using the Trig ratio.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Plug in the information present.
Opposite Leg
Hypotenuse
Adjacent Leg
Tan(55)=
Step 2Using the Trig ratio.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Insert a “1” under the Tan(55).
Opposite Leg
Hypotenuse
Adjacent Leg
=
Step 2Using the Trig ratio.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Cross multiply
Opposite Leg
Hypotenuse
Adjacent Leg
=
Step 2Using the Trig ratio.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Cross multiply
Opposite Leg
Hypotenuse
Adjacent Leg
20 ∙𝑇𝑎𝑛 (55 )=𝑥
Step 2Using the Trig ratio.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Enter that into your calculator..
20 ∙𝑇𝑎𝑛 (55 )=𝑥
Adjacent Leg
Opposite Leg
Hypotenuse
Step 2Using the Trig ratio.
5520 m
x
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
The calculator does all of the hard work!
2 8.56=𝑥
Step 2Using the Trig ratio.
5520 m
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
That is your answer.
28.56 m
Step 2Using the Trig ratio.
5520 m
𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎
Done!
28.56 m
They all work the same man! It works every time!!
