Right&Triangle&Trig&Review&

!
Warm&Up&3&What&IS&Trigonometry?& !&
1.!!Compare!the!three!triangles!in!the!box!below.!!Are!the!three!triangles!congruent?!!Are!they!similar?!!
Explain!how!you!know.!!!
!
CongruentTheyhave same angles
2.!!Label!the!sides!of!each!triangle!as!hypotenuse,!opposite,!and!adjacent!to!the!70°!angle.!
!
! 0 A so
!
SOH
!
6!
!
1754
I
!
! H
!
16.48
! 0.94
! 0
TOA
! H
!
6! 0
16.482.364
!
! H
! A
!
!
! A
3.!!Fill!in!the!following!table!with!the!ratios!from!the!sides!of!each!triangle.!!Round!the!divided!ratios!to!
nearest!tenFthousandth!(4!places!after!the!decimal).!!
!""!#$%& !"#!$%&' !""!#$%&
16.482794 =! 6
Triangle!ABC!
16.481754
=! =!
ℎ!"#$%&'(%
!""!#$%&
ℎ!"#$%&'(%
142
!"#!$%&' 1754
!"#!$%&'
!""!#$%&
6 2.797
8.22 94 =! 3
Triangle!DEF!
8248.77
=! =!
ℎ!"#$%&'(%
!""!#$%& g75.342
ℎ!"#$%&'(%
!"#!$%&'
!"#!$%&'
!""!#$%& 3 2.747
Triangle!GHI! =!10.99 =! 4 =!10.99
ℎ!"#$%&'(%
I 94 ℎ!"#$%&'(%
n 342 !"#!$%&'
4 2.747
4.!!What!do!you!notice!about!each!column?!!
! Each ulna is the same answer
5.!!Make!sure!your!yellow!calculator!is!in!degree!mode!(MODE!F>!Degree).!!!
!!!!!!Find!the!following!values.!!Round!to!the!nearest!tenFthousandth.! ! !
!
94
sin 70° =!_______! ! 342 !
cos 70° =!_______! 2.747
tan 70° =!_______!
6.!!Did!your!findings!from!the!table!match!up!to!the!calculator!values?!!Explain.!
!
yes eachanswer was thesame as thetable answers
**7.!!Using!the!side!lengths!in!triangle!ABC,!find!the!following!values!based!of!of!the!20°!angle.!!Confirm!using!
the!calculator.!
342 !
sin 20° =!_______! 0.94
cos 20° =!_______! ! 364
tan 20° =!_______!
 Trig&Ratio&Recap&
!
For!a!right!triangle,!the!sine,!cosine,!and!tangent!of!the!angle!!!is!defined!as:!
!
Csc!!!!!!!!!!!!!!!
sin ! = !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!cos ! = Sec
!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!
Cot
!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!tan ! = !!!!!!!!!!!!!!!!!!!!!!!! !
!
! Remember:!!
!
!
Example&1&Using&Trig&Ratios&
!
AZBEC B Sf is
! 17 17
! 82 5
152
! 69 d
225 17 0
is
H 17 17
5289
A
C 12
A
Sf
15 is8
0
&
Example&2&Finding&Missing&Sides&
Use!trig!ratios!to!find!the!missing!sides!of!the!following!triangles.!
1.! 2.! 3.! 4.!
! A
H !
! h o
O
! A
Ai ! Lo h A
sina.SE A
! !
7sin 0 47 !F
03
4 C y
!
o !
Esg !
Sin24 F 2 55 2 1
! F 9.83 F 11.47
!
Example&3&Finding&Missing&Angles&
reciprocal
To!find!a!missing!___________!in!a!right!triangle,!we!must!use!_____________!trigonometry.
Angle
!
! ! Ex:!!!!sin!(angle)!=!value! ! ! ! !!!"#!! (value)!=!angle!
! ! ! sin!(30°)!=!0.5! ! ! ! ! !!"#!! 0.5 =
!
Find!the!?!angle!measure!to!the!nearest!degree.!
1. 2. 3. 4. 5.

H
0
A
9 2 8605
7 41.4
Practice!
Find!the!missing!side!or!missing!angle.!!Show!your!setFup!and!solution.!
1.! 2.! 3.!
Tan62 !
9tan60 X
F 15.6

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4.! 5.! 6.!

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15.!

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